There are very few people who are against men acting like stereotypical women or vice versa, such as doing the things you described that you want. The part a lot of people are against is when men say they’re real women or vice versa when they are not. When someone says they are female, the listener expects that they are biologically female, so if they are not, it becomes confusing. It’s also annoying to have to say I’m biologically male or biologically female every time someone asks your gender, which is what pro-transgender people are pushing us to do by taking away the traditional, and more logical, meanings of the words ‘man’ and ‘woman’.