That may be, but there is also the episode where Kirk tries to talk the people of the planet Gideon into practicing population control.
I don't remember the discussion being all that specific, nor did I get the impression he was talking about abortion. I'm not saying Original Star Trek was perfectly conservative (there was that whole "no money" angle, of course) but it certainly had some strong conservative themes in many episodes. It was certainly better than the later Treks.
Of course it, it would make some sense for Kirk to be pro-choice. Most womanizers seem to be for obvious reasons ("Here's $200. Go take care of it for me.")