Is it possible a lot of modern society don't really understand Trans rights in general and actually just feign acceptance as an extension of gay rights?
Obviously this is the case.
Political and societal issues issues like this are inordinately complex and affect countless different classes of people in different ways. Trans rights activists, even if they aren't consciously aware of this, exploit it to their benefit. Typically by oversimplifying the issues into pithy, but false, slogans: "Trans women are women", etc. Similarly if you can paint your detractors as hateful bigots, people will mostly gloss past their arguments and go with whatever you say. This is also exploited by TRAs by reflexively calling any and all criticism as "transphobia".
Most people will see TRAs as a group who claim to be discriminated against, take them on face value, and move on. They don't have an especially deep understanding of the actual issues.
As you pointed out, they piggybacked of the LGB rights fought for and mostly won (at least in the west). On its face, the comparison is apt. Both homosexuals and transexuals are not in the hetrosexual majority - surely it makes sense to group them together? This is as far as the normie understanding goes. Of course, in reality, homosexuals are same sex attracted, whereas transexuals are people affected by various mental illnesses, autism, grooming, etc. Some even may have legitimate "gender dysphoria".
Is it even possible that many of these so called supporters secretly do hate trans people but simply never speak out because doing so would be social suicide and lead to them losing clout in their respective social circles and ruining their public image? How many of them secretly think deep down all of this is bullshit?
Again, yes. Obviously.
Much of transgenderism is bullshit. The entirely of gender ideology is bullshit. But sadly it's so much easier to passively go with the flow. The TRAs can endlessly spout "TWAW" and "Transphobe!" without engaging with the actual issues, but I have to base my arguments in reality. That is much harder work, and to a normie watching this, they're going to think I'm protesting too much, and isn't it just easier to be nice to the troons?
Outside of the farms, I don't publicly support troons. But I also don't speak up against them either. I don't have much of a personal interest in the issue, other than a respect for women and a disgust for misogynistic men pretending they're women by LARPing offensive and outdated gender stereotypes. If I stuck my neck out, it would get me kicked out of some circles I exist in.
This is itself, bullshit. Truth is truth. It doesn't matter who is saying "a man is not a woman and cannot become one", it's just a fact. But if I were a female athlete losing to troons, or a woman assaulted by some disgusting tampon fetishist, or a victim of grooming, it would be easier to make the case even if the arguments aren't any different. That is politics unfortunately.