After reading your edit I still have a few questions though.

I agree with you when you say that men don't experience institutionalized sexism (although I would argue the draft is the one and only example of institutional sexism they do face, although it is also sexist to women I would argue it isn't to the same extent in that one instance).

I don't understand you saying "Sexism is an institutional thing there is no "minor sexism'". I've always thought that there were multiple types of sexism/discrimination and it being institutional was one of multiple types, e.g I don't see how catcalling would be institutional sexism and it would fall under another category.

I'm also confused by what you mean by men being victims of prejudice as opposed to sexism. Are you saying that men literally can't be victims of sexism (no matter how small)? The Oxford definition of sexism is "Prejudice, stereotyping, or discrimination, typically against women, on the basis of sex" which absolutely makes sense to me, it makes it clear that women are the primary victims of sexism but does accept that men can be too, did I misunderstand your comment again or is is this not what you meant?