I differ a little.
The pro choice side passed from non existence to mainstream to discourse dominance in very few decades. Abortion is legal in ever more countries; the scope of its legality is also broadening; and private providers are expanding where governments don't have the resources to meet demand. International organizations (the UN and global NGOs) now openly support and promote abortion despite it being nowhere near their mandates. The pro choice side already won.
On the other hand, the pro life side have also evolved in our discourse and action. Although we still fight against legalization where it is on the agenda; and still promote banning it back where it's legal; most of our energy is now focused on the cultural side, in order to decrease abortion by directly lowering demand. We also have understood that we need to have explicitly pro life support institutions for pregnant women and mothers of young children in order to remove the pseudo socioeconomic arguments from pro choicers.
In the long run, I foresee we will lose the legal battle everywhere; but then we can win the cultural battle and lower the rates that way. Once that happens, it will be possible to push back on the legal front. But that lengthy process would certainly take decades. 100 years seems right to me.
The LGBT case is also different. They really didn't have people on their side in the beginning; and all throughout their societal support was lower than they make it seem -- even today. But several key things happened: first, they pressured with commitment and confidence the shrink establishment so that they became declassified. Second, you correctly point out, they infiltrated media successfully to promote their case through cultural means. Those two allowed them to artificially inflate their appearance of support and thus pressure the political and judiciary institutions into acceptance. A third factor which must be mentioned (because it's probably the greatest difference between them and us) is that they lost the fear of retribution and ostracism; physical, economic, social and legal. They considered that they had nothing to lose but their chains. Now, of course, this was made easier because they wanted to be with each other. In their couples, both were gay. Both faced the same issue. Both would win or lose simultaneously, together. In our case we cannot do that. The adult may realize they have nothing to lose; but the child faces consequences beyond those the adult can suffer and different from them. You have said that yourself: you don't mind doing time for loving a loli; but you very much mind what society would do to the loli for being loved. Gays never faced the same and that allowed them to be braver in their activism.