Key difference: Neonazis marching in Indiana aren't actually, physically hurting anyone. The moment they do, they cross the line from free speech and their action becomes illegal. Abortion IS violating someone's right, because you are choosing to terminate a life. The "woman's choice/woman's body" argument is nonsense becuase it ISN'T her choice because it involves another life, it isn't her body.
Of course it's a choice. You're talking about terminating something that cannot exercise any rights in its current form. The only person in control of that is the woman. It's her choice to terminate the "life," for lack of a better term, just like it would be your choice NOT to terminate the life. I'm not going to make arguments about whether or not that's fair, but that's the way it is. I have a cat. If I decided to kill my cat, it's not like he could scream murder and exercise his right to life, and the chances are that no one would charge in and stop me from killing my cat. I know that's a crude analogy, but I can't think of anything better. Also, I love my cat.
You're probably not going to convince anyone on here that abortion is wrong if they didn't think that from the beginning. I'd also suggest that you look into the history of abortion. Most of these heart-wrenching moral arguments are surprisingly modern developments.