Why then do I let people get to me when they try to make me out to be ignorant, unsympathetic, uninformed, whatever?
It gets to you because you are human. If they are too closed-minded to hear your perspective, than the best you can do is bow out of the conversation as gracefully as you can before you lose your temper and say things you will regret. That said, if you can keep your cool, you may be able to at least alleviate them of their prejudice, even if you cannot change their minds.

Pro-lifers, like anyone else I suppose, are not all alike. Some
are judgmental, unsympathetic, anti-woman fanatics. Some
are ignorant. Some
do care more about the baby than the woman. Most, however, know that to love the woman is to love her baby. We believe that we must defend and protect both. We know that women are faced with untenable situations are we are willing to work with them to find pragmatic solutions and to get real help. When they start going on about how pro-lifers are a laundry list of anti-woman adjectives, just say, “Yes. I met that guy too. He’s a jerk. Here is where he goes wrong…” Then introduce them to the attitude of a truly pro-life person.
It is worth noting that in general, those attacking you are likely on the defensive. The ones who lash out most angrily are usually the ones who have had abortions, or are very close to someone who has. The way I see it, faced with that realization you have two choices. Contempt, anger and judgement or sympathy and love. You can go on the attack, since they attacked you. Or you can offer to show them how you reach out. If they have had abortions, they are likely dealing with guilt, and grief that they do not think they have a right to acknowledge. Be kind. Did you ever read about Norma McCorvey? She was Roe of Roe V. Wade fame. She is now a pro-lifer. She came around because she felt the love of the pro-lifers.
I have not read your other discussion and do not have time to now, but this is how I have responded to attacks from people I know.
“I am sorry my post angered you so much. Clearly, we both have strong feelings about helping women and families in their distress. I’d be glad to discuss it with you, but I will not engage in a battle where neither of us is likely to change the other’s mind and we are likely to hurt feelings. Would you like to meet to talk about it? I suspect we have more in common than you think.” Or something like that, depending on who it is and how I was attacked. If I can, I like to compliment their passion for protecting women- which indeed is noble in and of itself.