I see nothing wrong with you trying to talk to her or ask her out. However, once she learns the disrespectful and entitled way you treat women, she will likely be uninterested. A "feminist" is someone, male or female, who believes in gender equality. Anything else you "think" a feminist is a negative stereotype. Clearly, you have a problem with women if you are hostile towards feminists. You also are under the misperception that a woman who is not initially interested in you will become so if you are around her and talk to her more-- and, therefore, you believe you are entitled to continue to approach women who are not interested. You do not have that right. And, usually, if a woman knows she is not interested right off the bat-- she will not suddenly become so later. I think your problem stems from a lack of respect for women. If you treated women like intelligent and independent people and stopped calling them "fragile princesses"-- then, perhaps, you would find women who were interested in you.

You have the right to ask this woman whether or not she is interested. However, based on the fact that she has ignored you several times, I think it's pretty clear she is not. Women DO send signals and do communicate through body language. If they're interested, they say hi, they lean in, they want to be around you, and they smile and laugh at the things you say. If they ignore you, it's pretty clear they are not interested. However, it is very hard to be "rude" to someone who is just saying hi-- so women are usually polite and will talk back so as not to come off as "stuck up." It's hard to say "leave me alone" to someone who hasn't done anything wrong just because you aren't interested in their company.

Speaking as a woman who goes to the gym 6 days a week, I can tell you that I am there to do my workout and leave. I HATE it when men or women approach me. I'm not interested in meeting anyone new at the gym. It is my sanctuary to be alone with my thoughts for that one hour a day. I hate being interrupted and losing that "me" time. I'm poliye when people try to talk to me, but I try to end the conversation as fAst as possible and then avoid them do it won't happen again. However, if they are persistent, I will eventually ask them to please leave me alone.