HI James - I am going through this now myself. My old tactic was to ignore, but it wasn't working out for me, because I would be angry inside, loose sleep, stress about it, etc. That was not good for my health.
So my new tactic, that I am working on, is NOT to ignore. If someone says something insensitive to me, I will question them on exactly what they mean, I will want a full explanation of why they said what they said. I will not let them off easy, like I have in the past, letting them insult me or hurt my feelings, without making them face up to the fact that they are hurting my feelings. I decided I will let them know exactly how it makes me feel.
They will probably stop making such rude comments. What do you think? For me it was my mother. And it turns out, she just wanted to make me feel bad, she didn't really want to explain herself at all, or talk about it. So I hope it will stop now that she knows she can't just make any old insensitive comment and get away with it without having to explain herself.
What do we have to loose? Try it, without getting angry, ask the person exactly what they mean, and tell them how it makes you feel. It's empowering, don't be afraid.