In the Congressional hearing on the HHS ruling on contraceptives (available here and here), the issue of tax dollars supporting government activities with which you disagree came up several times. It occurred to me, however, that since money is fungible, there's not reason why your tax dollars have to support a policy with which you disagree.
What if you had a line-item veto on how your tax dollars were spent? If you didn't want your tax dollars to (using the issue at hand), support taxpayer funded abortions, you could "veto" it. It wouldn't change the overall funding for any particular program--they'll just devote more of the tax money from someone who didn't veto that use to cover your veto. The funding would be the same, but your conscience would be clear.