To understand your feelings, I think we can look at the possible conditions of that bridge:
- The bridge isn't safe for him so you worry about the consequences.
- The bridge is safe for him but is not safe for you which sucks because sexism and double standards and you wish you could cross it too.
- The bridge is safe for both of you and so only fear has held you back from crossing it. Him walking across it fearlessly first could feel shameful to you left on solid ground still scared to cross.
I don't know what condition your particular bridge is in - there's all sorts of situational factors relating to career, relationships etc.
But regardless of its actual condition, I can see why watching him cross it is difficult. All of those possible scenarios are challenging in their own ways.
I recently expressed a mild science based defense of keeping women's sports female only to keep sport fair when it was discussed in a local social group chat.
I don't know if there will be negative consequences of that (some are vocally #bekind and act as if they assume everyone else is too) but I did feel better for it. A chunk of my discomfort was more about me keeping quiet rather than their reactions. I felt like I was a fraud and knew if the subject came up in person that I am a crappy liar and didn't want to be suddenly exposed and experience their hurt/anger or stay silent if it happened in person and betray myself. Now they know, and can choose to speak to me about it or not.
But I don't feel icky anymore for having secret forbidden wrong think thoughts. Because I (gently) stood up for my values (that females deserve competitive sports as much as male folk) I feel more comfortable with myself. If they were only friendly to me because they assumed I shared all their opinions then we're not the right people for each other. And that's okay.
I'm not saying things are as simple as that for you - careers, important relationships, safety etc are legitimate reasons to be cautious about this in the current climate. But in some circumstances, if you treat your opinions as worthy of respect, others may too - or you might care less what they think. The secretive thing is a hard place to be.