Github is actively within Microsoft ecosystem and all for the better of both sides from my experience.
Xamarin was crap before the Microsoft acquisition, it was improving at great pace afterwards and it's pretty integrated into .NET standard story (but still crap last time I used it 3 years ago) - I don't even see how you could say anything like they left them alone, feels more like they got rolled up in to .NET devision, again for the better of both (Mono was still the only solution for some scenarios until very recently even outside of mobile)
Github is still Github.
Of course Microsoft played a part in the progress. Try to be more generous with your nitpicking.
Github is a separate issue, they can't rebrand without huge value loss.
Is the Xamarin brand still strong?
Yes.
Nothing else is important. It is clearly a separate brand which is OBVIOUSLY going to be integrated (otherwise why buy it?)
But it remains a differentiable entity with the power of Microsoft behind it.
Continue nitpicking.