Noah Webster on '-er' and '-re' word endings (chiefly '-ter' and '-tre')
One dedicated opponent of -re endings of the type that the poster has in mind was Noah Webster. Here is his discussion of such words in A Compendious Dictionary of the English Language (1806):
We have a few words of another class which remain as outlaws in orthography. These are such as end in re, as sceptre, theatre, metre, mitre, nitre, lustre, sepulchre, spectre, and a few others. Most of these have found their way into our language from the Greek and Roman, through the channel of the French. This termination is common in the Saxon as well as the French, and probably the final e was pronounced after the consonant. However this may have been, English writers have unanimously formed a different analogy by transposing the letters, so that the re in sceptre can not be considered as an English termination. And it is among the inconsistencies which meet our our observation in every part of orthography, that the French nombre, chambre, disastre, disordre, diametre, tigre, chartre, arbitre, tendre, fievre, entre, mostre, and the Saxon hongre, and hundreds of other words should be converted into number, chamber, disaster, disorder, &c. conformable to the pronunciation, and that lustre, sceptre, metre, and a few others should be permitted to wear their foreign livery. This is the more surprising, as the most distinguished writers of the last and preceding centuries, Newton, Shaftesbury, Dryden, Prideaux, Hook, Whiston, Bolingbroke, Middleton, &c. wrote these words in the regular English manner.
...
The present practice is not only contrary to the general uniformity observable in words of this class, but is inconsistent with itself; for Peter, a proper name, is always written in the English manner; while in salt petre, the word, derived from the same original, is written in the French manner. Metre also retains its French spelling word in composition, as in diameter, barometer, and thermometer, is conformed to the English orthography. Such palpable inconsistencies and preposterous anomalies do no honor to English literature, but very much perplex the student, and offend the man of taste.
Webster takes another run at the same topic in his full-length An American Dictionary of the English Language (1828):
A similar fate has attended the attempt to anglicize the orthography of another class of words, which we have received from the French. At a very early period, the words chambre, desastre, desordre, chartre, monstre, tendre, tigre, entre, fievre, diametre, arbitre, nombre, and others were reduced to the English form of spelling; chamber, disaster, disorder, charter, monster, tender, tiger, enter, fever, diameter, arbiter, number. At a later period, Sir Isaac Newton, Camden, Selden, Milton, Whitaker, Prideaux, Hook, Whiston, Bryant,and other authors of the first character, attempted to carry through this reformation, writing, scepter, center, sepulcher. But this improvement was arrested, and a few words of this class retain their French orthography; such as metre, mitre, nitre, spectre, theatre, sepulchre, and sometimes centre. It is remarkable that a nation distinguished for erudition, should thus reject improvements, and retain anomalies, in opposition to all the convenience of uniformity. I am glad that so respectable a writer as Mitford has discarded this innovation, and uniformly written center, scepter, theater, sepulcher. In the present instance, want of uniformity is not the only evil. The present orthography has introduced an awkward mode of writing the derivatives, for example, centred, sceptred, sepulchred; whereas Milton and Pope wrote those words as regular derivations of center, scepter, sepulcher: thus, "Sceptered King." So Coxe, in his travels, "The principal wealth of the church is centered in the monasteries." This is correct.
With regard to the particular words that he mentions in these two discussions, Webster is quite consistent in promoting the -er form over the -re form. Thus, for example, his 1806 Compendious Dictionary has entries for these words:
center, luster, meter, miter, niter, saltpeter, scepter, sepulcher, specter, theater
In none of these instances does the -re form appear as a variant spelling option or as a cross-referenced ghost entry. This may be because the definitions are so short in this dictionary that a reader can quickly scan from where the -re form would have appeared in alphabetical order to the place where the -er form is located, or it may be because Webster was so dedicated to the spelling he preferred in each case that he didn't want to give the less desirable spelling any exposure.
The 1828 An American Dictionary remains firmly committed to the -er spellings of these same words, with primary entries for the following spellings:
center, luster, meter, miter, niter, scepter, sepulcher, specter
In the 1828 dictionary, however, Webster's zeal seems less extreme. For one thing, he adds a brief cross-reference entry for metre, directing readers to the primary entry at meter. And perhaps tellingly, the entry for luster appears not between the entries for lust and lustful but (out of alphabetical order) between the entries for lustration and lustrical, suggesting that the author made a late-galley correction of the spelling from lustre to luster. More significantly, Webster introduces dual-option entries for saltpater/saltpetre and for theater/theatre, albeit with the -er form listed first in both instances.
Webster on -cre and -chre words
So much for the words that Webster himself brings up as examples of problematic -re orthography. But what about the "few others" that he mentions in his introduction to the Compendious Dictionary? All but one of the specific examples he cites end in -ter/-tre; the only exception is sepulcher/sepulchre. But as it turns out words ending with a hard k sound preceding the -er/-re ending are fairly numerous in their own right, although less so than the words ending in -ter/-tre that he devotes most of his attention to. Consider the following examples:
acre, chancre, euchre, lucre, massacre, mediocre, nacre, ochre, sepulchre
In the introduction to the Compendious Dictionary, Webster notes that French influence on orthography rendered the simple Saxon equation of c with a k sound unsupportable when the letter appears adjacent to certain vowels:
The Norman conquest however effected a change in the power of c, and established it as the equivalent of s before e, i and y. This, like most innovations, introduced confusion, and rendered it convenient or necessary to use k in all words in which the power of k was wanted before those vowels.Thus the Saxon cepan, to keep; licciam, to lick; licean, to like; locian, to look, were converted into the present English words; and in many words, k usurped the place of c without a like necessity, as book from boc. Hence we find that in most of our Saxon words, k is written at the end, after c or in lieu of it; and we cannot, without it, form the past time and participle of verbs; for liced, loced would lead to a false pronunciation.
But the c in all of the -cre words listed above is subject to the presumption of being pronounced as an s rather than as a k when the spelling changes from -cre to -cer. And a similar presumption of "ch as in church" sound might attach to -cher spellings, in light of words such as poacher and preacher, making that sound more likely that a k sound to attach to a new -cher spelling. So how did Webster propose to spell these words? Here are the 1806 Compendious Dictionary's spellings of each -cre or -chre word listed above:
acre or aker, chancre, [no entry for any spelling of euchre], lucre, massacre, [no entry for any spelling of mediocre], [no entry for any spelling of nacre], ocher, sepulcher
And here are the spellings that appear in the 1828 An American Dictionary:
acre, aker, chancre, [no entry for any spelling of euchre], lucre, massacer or massacre, [no entry for any spelling of mediocre], naker (as well as a cross-reference entry for nacker, directing the reader to the full entry for naker), ocher, sepulcher
Perhaps Webster felt that the existence in English of canker and cancer obviated any need to make the orthography of chancre less French. But why did he give lucre and massacre a pass in 1806 (and lucre again in 1828)? Moreover, aside from aker, his spelling innovations in the 1828 dictionary (massacer? naker?) seem neither consistent with pronunciation nor orthographically predictable.
Where popular orthography has gone
Today, all of the -ter spellings that Webster championed remain dominant in U.S. English orthography, according to Merriam-Webster's Eleventh Collegiate Dictionary (2003), but with some variant spellings accepted as common in the U.S. rather than being identified as "chiefly British":
center, luster or lustre, meter, miter or mitre, niter, saltpeter, scepter, sepulcher, specter or spectre, theater or theatre
The picture is murkier for the -cher spellings that Webster preferred. Again from the Eleventh Collegiate:
euchre, ocher or ochre, sepulchre or sepulcher
In two of the three words, the -chre spelling is either unchallenged (euchre) or preferred (sepulchre).
As for the -cre respellings, Webster's idiosyncratic attempts at orthographic reform have completely bombed, according to the Eleventh Collegiate's listings:
acre, chancre, lucre, massacre, mediocre, nacre
There is no sign that aker, massacer, nacker, or naker has even the slightest toehold in U.S. English spelling. Perhaps, when push came to shove, U.S. English writers found it easier to read the -cre spellings as equivalent to -ker than to build multiple forms of -cker, -ker, and (counterintuitively) -cer to replace words that end in -cre but have varying characteristics otherwise.
That, at any rate, is a small part of the background behind the mixed presence of words in U.S. and British English with -er and -re endings.