Strictly speaking, "profane" simply means something that is not sacred.
Generally speaking though, "profane" and "profanity" are taken to mean vulgarity or offensive language or behaviour. At the very least, outside of a discussion on religion, one would assume that's the meaning.
When did this happen? Was it a simple subtle shift or was it brought about by something?
The original meaning is that of “secular”, which evolved the “offensive” connotation from the 16th century apparently the from “Old French profaner, prophaner (13c.), directly from Latin profanare "to desecrate, render unholy, violate," from profanus "unholy, not consecrated".
mid-15c., "un-ecclesiastical, secular," from Old French profane (12c.) and directly from Latin profanus "unholy, not consecrated," according to Barnhart from pro fano "not admitted into the temple (with the initiates)," literally "out in front of the temple,"....... Sense of "unholy, polluted" is recorded from c. 1500.
The extension of the meaning came with the term profanity, a term which became popular from the 19th century with the more general sense of vulgar language.
c. 1600, "profaneness, quality of being profane, profane language or conduct, ………… Extended sense of "foul language" is from Old Testament commandment against "profaning" the name of the Lord. Apparently a rare word before 19c.
(Etymonline)
Its use in English has always been related to that which is either not "of God/the Church" or opposed to the Word of God/the Church.
I would go so far as to say that any other use is figurative but still subjectively offensive.
The earliest record in the OED of profane is mid-15th century:
Profane
1. Of persons or things: unholy, or desecrating what is holy or sacred; unhallowed; ritually unclean or polluted; (esp. of religious rites) heathen, pagan. In later use sometimes merging with more general meaning at sense A. 3.
c1450 Three Kings Cologne (BL Add.) l. 767 in Archiv f. das Studium der Neueren Sprachen (1912) 129 67 (MED) Ther-in to come þay suffrede neuer none, Bot called it curste, vnhappy and prophane, Till Constantyne and his modir it wane.
Given there is only ~25 years between the records, I would hazard that the neutral sense (below) was extant at the same time:
2.a. In neutral sense. Not relating or devoted to what is sacred or biblical; unconsecrated, secular, lay; civil, as distinguished from ecclesiastical; as profane history, profane literature, etc. Frequently contrasted with sacred.
1474 in M. Napier Mem. J. Napier of Merchiston (1834) 37 n. That quhar..scho schapis to procede agains him befor you in the spirituale courte..we..commendis, that the said action is prophane & is decidit & finaly endit befor the said lordis.
The negative religious sense appeared in the early part of the 16th century, probably in response to The Reformation and, later, King James I/VI.
3. Of persons, behaviour, etc.: characterized by, exhibiting, or expressive of a disregard or contempt for sacred things (esp., in later use, by the taking of God's name in vain); not respectful of religious practice; irreverent, blasphemous, impious; (hence, more generally) ribald, coarse, indecent. Now the most common sense.
1568 A. Scott Poems (1896) xxxiv. 86 Ȝor prettikes ar profane, Puir ladeis to supplant.
1614 R. Brathwait Schollers Medley 17 So should our prophane Pamphleteers restraine their libidinous writings more.
A wider sense appeared in the early 17th century:
2b. Of persons: not initiated into religious rites or sacred mysteries; (in extended use) not participating in or admitted to some esoteric knowledge or society; excluded, uninitiated, ‘lay’.
1612 J. Cotta Short Discouerie Dangers Ignorant Practisers Physicke 4 Wholesome remedies in vulgar and prophane hands.
So the answer to your question is that the your meaning of "profane" arose sometime before 1474, and the more general a few years earlier.
