These same people also pay for police and military (some 50% of the federal budget goes to the military, last I looked). The military is presently actively engaged in killing people, but at all times at least engaged in thinking about how to do it, that is a strong violation of judeo-christian values. Additionally soldiers have been known to rape and murder innocents. You can't take responsibility of what someone else does with your tax money, it stops being yours when you fork it over. You vote for the person who will best represent your morality, and hope for the best. Jesus set that precedent in the bible ("Render unto Caesar...") over very similar concerns brought up by Jews.
Rational Christians would not have any issue with this. Rational Christians would has a more sensible view on abortion (i.e. the unfunded mandate that all children must live....to suffer in poverty? that children born with detectable birth defects must be born, and left without medical care?). They may not support abortion, but they certainly would not allow an innocent to suffer through apathy. In any event, that's not the group doing the talking. Rational Christians, I could probably find a middle ground with, even if I don't believe in their magic.
However when you put the decision in their own hands, yes, some will not want to fund abortions, and will not want to fund contraception, etc. In this case you're asking them to actively pay for what they don't like, but not giving them the tools to properly rectify the problem. I still think they're wrong, you can't chop logic morality, but it's in the defensible region of "things I can control, and things I can leave to God". As far as I'm concerned the rhetoric of "You are all sinners" is less a condemnation of mankind, and more a statement of fact: we cannot help but sin, we lack the tools. We can however choose how to sin and try to manage the consequences. But not being religious, I am not sure how that matches the various world-views of all sects. It seems like choosing not to commit the sin of murder may be the greater sin when the victim was about to walk in to a school with an assault rifle, for example. Not paying for the abortion may be the greater sin then bringing children in to the world who will suffer, and who will spawn more children who will suffer.