I think that war is morally objectionable and the government shouldn't pay for it. You see how well that goes. What's the difference, exactly?

Besides, I know plenty of religious people who may even personally think abortion is morally objectionable, but still have no problems with it being legal (and I assume this would also extend to it being covered by Medicaid/other government funds, although I admit I have not asked). There are a huge number of people who don't think their moral standards should apply to everyone.