First, note that tax money wasn't used to buy the art. The exhibitions were privately funded. The public funds went to the upkeep up the public building in which the art was housed, as well as some staff.
Of course, I don't really believe that the public money used to pay for the building is inconsequential, but the point is that any private exhibitor can petition the museum for space. So, it looks like the public at large would like that have that voice.
Still, even with private funding, the government should continue to maintain an arms length distance from the museum because it's much better for it in the long term. Art provides useful critique of common society that a goverment--as the strong arm of that society--must be responsive to.
That's why democratic societies created press freedoms, but we all know what has happened with the press as its industry has pined in recent decades. The profit motive has consolidated power and reduced competition to who is more efficient at feeding the mainstream. Works of conscience cannot survive.
However, as I said, it's necessary for works of conscience be artificially given prominence in the marketplace or else the society risks breaking the feedback cycle that keeps it on track. Studies (*) have shown the richer a society the more insular it becomes, incestuous and xenophobic. The irony is that the richer societies can better afford to pay for public art.
Many people assume that counterculture ideas that were truly good could survive in a pure market. That is false. First, the Theory of Second Best refutes the pure market in an important and relevant way. Consider the difficulty indie musicians have breaking through the RIAA. Secondly, by definition, counterculture ideas aren't as profitable as mainstream ideas. For a profit motivated promoter, counterculture isn't worth the time.
The reason why the public pays for art and critical organizations is to keep itself from becoming too warm in the fleece that covers its eyes. So, while the ideas of those cultural institutions may be offensive to the Institution, that's the whole point. Even if the ideas in the art are bad, the idea of art is good.
So, it would be completely inappropriate for the Mayor of New York to exert political influence over his city's museums, but Guilianni as a citizen is free to combat the ideas directly.
(*) I don't have the studies handy, but I found a decent op-eds from Claude Moisy. If you plied through Journalism Quarterly you will probably find the studies that track foreign news content from year to year. There are also  and 
"Look! You're free! Go, and be free!" and everyone hated it for that. --r