I don't actually know, in person, many anti-trans people who have had problems with being 'de-accepted'[1] ((<=edit: "de-accepting" makes more sense here, if anythin... I think I munged sentences about both sides together. But neither anti-transers going notably more anti- nor transers suffering more anti- backlash must have been my intended gists, respectively. Does this help? No, probably not.)) Though I've known people who are 'anti-' in various illiberal ways that likely makes them perrenial objectors to the vague idea of trans-ness amongst all the other kinds of 'not my kind of person' bigotry (possibly, in some cases, actually self-hate from peer pressures). Perhaps I'm just not that observant, though, to the subtlety of drifting opinions.
I do find it ironic that there are vocal members of minorities(/traditionally oppressed) who have strong opinions against even smaller slices of minorities (often with similar problems of acceptance by the 'majority' to themself) beyond what I'd see as rational. Whether that's the first two of the original LGB who dislike the third, or 'white' LGBTs who are outright racist to non-white LFBTs, or the uncompromisingly trans-exclusionary subset of women.
I think it's more the 24-hour-news and/or echo-chamber effect that it is more obvious or (seemingly) promoted, though. Possibly it's just more 'acceptable' to admit (even on an anonymous survey) that you have such a low-volume[2] personal discrimination, and an opinion you probably didn't even learn to have (or was just indistinguishable from background homophobia) in days gone by, but now you've got evangelistic fearmongering highlighting the rare cases when trans(-identifying) individuals are of the predatative variety rather than being physically and emotionally more vulnerable even than the typical woman might be.
Disclaimer: This is my gut feeling, possibly as uninformed as anyone else not actually in the shoes[3] of any of those involved. With no reference to any such cross-era survey results, at all. In the first part, I'm not trying to 'cis-splain' anybody's own experience (nor more tradaitionally man-splain), and I'm just giving my impression from my own singular and statistically insignificant viewpoint. I'll have to accept full ownership of any hole I've just dug myself into, therefore.
[1] Not openly, anyway. Of the handful of actual trans individuals I can speak of (and, obviously, for one reason or another have known to be so), I haven't been there to see hostility at first-hand. What problems they encountered in everyday life I can only imagine. And one of those individuals was for some time a member of a sports club I'm in but may have left due to adverse comments by some other member that were never made in my presence.
[2] With a top-end estimate being that it involves slightly less than 0.5% of the population. I mean, it's practically a victimless bigotry, at a level below that of run-of-the-mill antisemitism and maybe slightly above a distrust of 'gypsies', amirite?
[3] It would be crass to substitute "shoes" with some terminalogically feminine version of the attire, but it did of course momentarily occur to me. Before I decided not to. Before then deciding to explain here that I decided not to, as full disclosure. Why I additionally decided to explain all further meta-explanations, I'm afraid I cannot explain.