No it doesnt. hate speech is not protected speech never have been and should never be. same way slander etc isnt protected speech. What free speech is there to grant you is the protected right to protest and petition your government on issues and i can promise you hate speech is not part of those protected issues
The key issue here is GOVERNMENT since free speech does never apply in the private sphere a private company have no reason to keep your voice of hate speech open if they so choose. Same reason you can be silenced and banned on a message forum like this, no free speech protections in place and same goes for youtube