Word for: "dislike of people that has same gender as speaker"

Misogyny/Misandry can absolutely satisfy the 'same gender' requirement if applied appropriately. If you're looking for a word that can be applied across the board for what feminists call 'internalized misogyny', though, I don't think there is one.

It may not yet have much currency, but cisgenderphobic is already out there!

The word is formed by extrapolation from, for example, cisatlantic (on the same side of the Atlantic as the speaker), and cisalpine (on the southern side of the Alps).

As can be inferred from the definition of cisalpine, the cis- prefix already carries overtones of prejudice/bigotry - the assumption being that anyone living north of the Alps would be too ignorant to use such erudite terminology, so it's okay to define this side of the Alps as "south".

It's been used about a total of three times in the universe, but autogenderphobic would be recognized by people who are good enough at their Greek and Latin roots. All twelve of them.

Gynophobe (or gynephobe) means 'someone who fears, hates or has contempt for women' (see http://www.thefreedictionary.com/gynophobe ).

Can also be gyn(a)ecophobe (see http://www.oxforddictionaries.com/definition/english/gynaecophobia ).

I don't believe there's a specific standard term for woman-on-woman hatred or someone who perpetrates it.