Fear of what others will think can be perfectly rational. But I don't think it's that so much as it is what the consequences of the negative will be. What it really is, is fear of what people will do if they think something that gives rise to an adverse reaction. It's a self preservation instinct, and entirely understandable.
Thoughts are thoughts. But actions that arise from those thoughts... that is the scary thing. People's unpredictability based on their thoughts... fear of that unknown. It's a primal human instinct to want to protect oneself. Or to protect people around you. To not want to be hurt. That's a perfectly healthy thing. We've been doing it for thousands of years.
I think the best way you can deal with that is by encouraging belief in oneself, and the capacity to deal with people's reactions to things. By giving oneself confidence. And building up self-esteem. The absolute worst thing you can do is hate yourself for feeling that way. Because it just reinforces a cycle of negativity that never seems breakable.
Ask yourself how many people feel that if they aren't strong enough to get over what being themselves may lead to with other people, that they aren't strong enough to actually be themselves? I'm betting it's a pretty common thing. "If I can't deal with this, how can I deal with anything else?"
That is blaming yourself for other people. It's feeling yourself to be weak for not wanting to be hurt, and caring that your feelings/physical self/sense of self may be subject to punishment. That is not weak. It's human. And the first step to getting past it is realising that it doesn't make you weak, or anyone less, for feeling that way. When you can do that, then you can start to see what you actually can do, instead of what you feel you can't.
That's the trouble with low self-esteem. And often low self-esteem is tied in very closely with being trans. It's a downward spiral. We reinforce the cycle of negativity and feel like we're less and less capable of doing anything. And scared that people will act in the worst possible way. Which in turn leads to self-hate for not doing anything. Which leads to even more of a feeling that people would think the worst... and so on, and so on.
Break that by realising that is isn't weak. It doesn't make you a coward. It doesn't mean you aren't capable of... well, of anything. Fears only have a hold of you while ever you feel you aren't capable of dealing with them. But I've been around here long enough to see firsthand that people can be incredible. And deal with things that they don't think they can in their wildest dreams. It just takes a bit of self belief.
*extra big hugs*
