I'm an ex-feminist who was unplugged in her late teens and I've grown in an environment that encouraged strong independence and undervalued emotional support too. It has forced me to be as sharp as I could and to improve myself all the time because I was constantly aware of the fact that if I didn't look out for myself, nobody else would. I can relate very well to your experience on some level.

You speak a little abstractly about what your "manly", "feministic" qualities are, so it's a little difficult to give you specific advice.

What is it exactly that makes friendship with feminine girls so hard?

You speak about being intelligent, sharp, smart, self-improving, intellectual, but all these things are not bad and they're not at odds with being feminine. What matters is how you express these traits. Is it that you overcompensate for your fear of vulnerability by being very aggressive? Are you callous towards others? Or condenscending because of your intellect?

You won't lose your power by becoming more feminine. Masculinity gives you power over others through intimidation, but femininity gives you power through likeability. Others will do things for you because they appreciate you and like the way you make them feel about themselves.

That's why it's important to smile, to not assume the worst in people, and, in case there's a conflict, express criticism in a way that is the least likely to hurt other people's feelings. More concretely, this means avoiding pejorative wording or personal attacks.

I need to be in control and I fear vulnerability too. It's a legitimate fear that you have because there's true danger in being vulnerable. But there's a remedy: lower the danger. Surround yourself with positive people with a strong moral compass, people who seem trustworthy. Avoid the ones who are the most likely to feed your fear of getting hurt by disappointing you.

You might have to search for a while before you find these people, but they're there. Look for girls who are very ladylike (graceful, positive, non-judgemental) and avoid hanging out with the type of people that you don't aspire to be like. Usually, the crowd you hang out with rubs off on you whether you want it or not, so surrounding yourself with people who embody what you want to be is very important.

As for the most practical things like looks and cooking, jules991 answered that well. Finding friends who can teach you is better, but textbook or internet tutorials can help a lot.