Girls never genuinely get friend zoned. It's just an excuse guys use when the girl is 1) Ugly or 2) Crazy as fuck. Most guys will just hook up with/ fuck a chick, then ignore them, instead of friend zoning them.
Regarding your skiing problem; if you are doing tricks that can compare to most other tricks done in the park your in, than people will take you seriously. It's no different with guys. People doing tricks worth being recognized, will be recognized, regardless of gender (unless you surround yourself with people who are sexist, which most people are not.)
Regarding your claim that girls can do anything guys can do; this statement is not true. I realize that sounds sexist, but bare with me. That statement is not true, and neither is the statement, guys can do anything girls can do. Scientifically, guys are naturally stronger, and girls are naturally more flexible ect. This does not mean that every single guy is stronger than every single girl, and every single girl is more flexible than every single guy. This just means that if a guy and girl were exposed to the exact same external conditions and stimuli, the male would be slightly stronger, and the female would be slightly more limber, along with other differences such as tolerance to cold and pain.
These slight advantages have slowly created gaps between the skill levels on men and women in different fields. Due to this, there are things that some guys can do currently that no girls can do currently, as are there things that some girls can do currently that no guys can do.
Sparknotes: I just denied each and every one of the OP's claim.
