This is a bit of a conundrum...
This is a terrible difficult question and I think there is no answer to it that satisfies everyone. And when there is no satisfactory answer to something I am hesitant to reply because the question might be invalid. Your question suggest either a positive or negative answer, and because of this I cannot answer that because I cannot speak for everyone. It is like asking: will everyone one day love the color pink? that question is problematic and could better be rephrased differently, or not asked at all.
I do want to attempt to give my answer though, so here it goes for me:
I think the general population will never accept T's uniformly as a whole at any given moment. They might tolerate us, which means they let us in their hierarchy or caste when they understand that we are not a threat to them. They might figure out how to exploit us financially, and therefore seemingly accept us. But complete acceptance seems a Utopia. If you want to know why, then you have to dig deep down into biology, sociology and a miscellaneous mess of psychology.
But for me, I don't want to be accepted. Because acceptance is actually a way of subordinating us into a caste we're already in, but on THEIR terms.