Guiuliani does have a very liberal approach but that does not mean you shouldn't vote for him. You should vote for the candidate who is the closest to what you want for the direction of this country. If he is up against a very conservative Republican then the voting is going to be very split.
A majority of people I've met in my lofe fall into a socially liberal, fiscally conservative mindset. Not to say that perfectly describes Guiuliani, but beings socially liberal is a general trend that's probably for the better. Government should stay out of a lot of social issues, and social attitudes should have little to do with candidate selection.
An American has the right to vote for whomever he or she would like to. One can say that a person is wrong for voting a certain way, but more often than not that person's opinion will be clouded with what Orwell called, "the smelly little orthodoxies contending for our souls."
Thousands of people will vote for Guiuliani and thousands of people will vote against him. his socially liberal attitudes shouldn't necessarily cause you to vote against him, especially if you agree. However, if you have a different opinion that's matched by another candidate, then you should consider voting for that person.
It is so uncommon for us to have truly caring and compassionate politicians. Guiuliani may have some attitudes that align with social liberalism's, but I do not believe that is a reason not to vote for him. If anything, it is an excellent reason to vote for him. Guiuliani did a great job in New York and he can do a great job for the rest of the country.