This answer is a follow-up to the already excellent answer by Nat. Its purpose is to clarify some aspects of the background of the issue, and to incorporate into an answer some of the insights that have been articulated by various contributors in the comments (which are at risk of being deleted by the moderators as excessive).
The view that the term sexual preference is offensive is based on the following three premises:
(1) The belief that being gay (which, within this answer, includes being lesbian and being bisexual) is not a matter of choice is more conducive to the recognition of gay rights than the belief that it is a matter of choice.
(2) Using the word orientation in this context better fits the belief that being gay is not a matter of choice than using the word preference; the word preference is, on the other hand, better suited to the belief that being gay is a matter of choice.
(3) (1) and (2) are so obvious that the only purpose anybody could have in using the term sexual preference is to actively undermine gay rights.
If one accepts (1), (2), and (3), and one supports gay rights, one will likely find somebody's use of the terms sexual preference offensive. Should one accept (1), (2), and (3)?
Regarding (1), it should be noted, first, that the belief that being gay is a matter of choice does not logically entail any kind of opposition to gay rights: as has been pointed out by thieupepijn in a comment, one may believe that being gay is a matter of choice and that this is a perfectly OK choice to make, a choice that everybody has the right to make without being subjected to any disadvantages for it. It is, however, still possible that as a matter of psychology and sociology (rather than logical entailment), people are more likely to support gay rights if they believe that being gay is a not a matter of choice. Whether (1) is ultimately true is thus an empirical matter, which puts it outside the scope of this site. What is relevant to the question posed by the OP is, however, that the belief in the offensiveness of sexual preference depends on (1).
Regarding (2), it should be noted that there is nothing self-contradictory about saying that one is oriented towards something because one has so chosen; the meaning of oriented does not rule that out. There is also nothing self-contradictory about saying that one prefers something because one is so constituted that one can't help preferring it. To borrow the example from Jjj's comments, one may say that one prefers red wine to white wine, without having any idea as to why one does. If it were to be discovered that there is something in one's genes that makes one prefer red wine, that would not make one stop saying that one prefers red wine, and it certainly won't lead one to start saying the one is now oriented towards red wine. Thus if there is a connection between using the term sexual preference and believing that sexuality is, in this respect, a matter of choice, that connection is not a logical entailment, but at most a psychological connection: the term arguably 'might kinda subliminally push people toward thinking of sexuality as a choice', as Nat has so eloquently put it.
So, even though (1) and (2) may be true, they are not so obviously, unquestionably true that everybody who uses the term sexual preference should be immediately presumed to be doing so out of a desire to undermine to gay rights. In other words, (3) is not true. It is perfectly possible to disagree with (1) and/or (2), or to be uncertain whether (1) and/or (2) are true, and so use the term while wholeheartedly supporting gay rights.
(To avoid possible misunderstandings, I should make it clear that this answer, as befits this site, and like the other contributions so far made to this page, deals with the question only as a question about the meanings of certain English words; it is not intended to imply anything whatsoever about the current political developments in the United States that have prompted the question.)
