Take embryonic stem-cell research. President Bush has limited taxpayer funding of this research on right-to-life, not fiscal-conservative, grounds. He's not against all federal financing of the research, but he doesn't want to expand what's already being done. Conservatives generally support him.
Liberals oppose Bush's stance because they like funding what they favor, and they favor stem-cell research.
They often describe Bush's policy as a ban on research. That's not true. Researchers at Harvard, Vanderbilt, and other private institutions already spend millions on this work.
Clearly there's a difference between private and government financing, and someone can logically favor the first while opposing the second.