The problem with Contrapoints (and that video is a perfect example) is that their style of 'debate' is to set up a bunch of straw men and then knock them down as bitchily as possible under the guise of being 'witty'.
Yes. Whereas our counterpoint, as it were, would be someone like Magdalen doing a response video. The difference being that, it's actually a response incorporating (albeit edited) the actual words and arguments of the other side. Most Magdalen videos are under 50% Magdalen. Most Contrapoints videos are 99% Contrapoints. 
This difference was obvious to me within an hour of looking into the debate when I became aware of it. One side clearly knew the other's position, was prepared to present it, and had arguments against it. The other side either didn't know their opponent's position or were willfully misrepresenting it.
That immediately made me very much inclined to trust the GC side.
The GC's villains/concerns were real - "males already going into women's prisons?" Sounds implausible... nope, it's happening. TRA villains/concerns generally weren't - "murder epidemic of trans people?" Sounds implausible... ah, totally false.
I'll take Contrapoints seriously when they start taking their opponents seriously.
Time for my John Stuart Mill quote again:
“He who knows only his own side of the case knows little of that. His reasons may be good, and no one may have been able to refute them. But if he is equally unable to refute the reasons on the opposite side, if he does not so much as know what they are, he has no ground for preferring either opinion... Nor is it enough that he should hear the opinions of adversaries from his own teachers, presented as they state them, and accompanied by what they offer as refutations. He must be able to hear them from persons who actually believe them...he must know them in their most plausible and persuasive form.”
The vast majority of TRAs do not remotely pass that test. If you're sitting and listening to Contrapoints though, you're trying :)
I believe Contrapoints knows actual GC arguments quite well - you'd have to, to dance around them so gracefully. But Contrapoints' viewers do not, thanks to people like Contrapoints' misrepresentation and the bizarre "block and stay safe!" mentality.
So this is not a proper civil rights movement - the people who know what they're talking about aren't trying to debate and convince of their arguments - they're trying to whip up a mob against an imaginary enemy, trying to keep the people on their side misinformed, and drive their policies through by basically emotion.
And there is a debate - it's largely a balancing of individual freedom versus societal harm. The TRAs are on the neoliberal "freedom" side, the GCs caring about the societal harm. (And the "societal harm" is of course to other individuals!)
I think I probably tend more towards defaulting to liberal/freedom principles than many on the board, but the harms of the TRAs' desired policies are far too egregious for me. They're trying to get many nonconsenting people dragged into their roleplay, and not respecting their autonomy and rights.