Why did you ignore all my other examples?
For three reasons.
1) They are taking us further and further from the OP and muddying a pretty simple argument - suggesting 'gay's can change' is wrong. Expressing that view should be challenged and not defended under freedom of speech. Disliking a video is a way of challenging this.
2) Your first example:
What if a gay man says his gay relationship is a choice? Should he be charged with a hate crime too?
I've worked with a number of gay men who have all said that they have felt that way for their entire life. So unless you can provide an example of this then I'd suggest this is a strawman argument.
3) Lastly the other two examples:
Climate change denyer - whilst dangerous for our planet this doesn't psychologically harm an individual - unlike suggesting they can chose their sexuality. So context is important. Expressing such a view should be challenged and not defended under freedom of speech.
Antivaxxers - you jump straight to jailing them. Why? Expressing that view should be challenged and not defended under freedom of speech.
Of course if death results then yes, they should be jailed:
Your view seems to be 'let them say what they want as this is freedom of speech - or you'll end up jailing them all'.
That feels like a pretty extreme position to take.