Is this a fallacy if so, what is it called?

If you do not believe in something on a moral level, you obviously believe that should apply to all of society.

Is that true? Because that sounds like a hasty generalization to me.

I know of many folks (Vegans, Celibates, penitents, etc.) who believe things for themselves, but would never dream of imposing that belief on others.

It is fallacious. Before we get into why, this line of reasoning does make more sense in any context where nobody is being hurt--a victimless crime. The best example is gay marriage. If you don't believe in gay marriage, don't marry someone of your same gender. Some pro-choice advocates will reject the claim that in abortion there is a victim. At one extreme, the "victim" is a cluster of cells whereas at the other extreme the victim can be a fully-formed baby capable of living outside the womb (as in late-term abortions). Also, some pro-life advocates might hold a religious view that at the moment of conception there is a "soul" and therefore a victim. So with abortion, this argument is questionable and debatable.

Ultimately, in any context, we are dealing with the fallacy of equivocation . When someone claims that they don't "believe in" abortion or even gay marriage, "believe in" refers to a moral position whereas in the argument it is meant to mean a preference , as in "I prefer vanilla to strawberry." If one prefers, vanilla, then they should not order strawberry--makes perfect sense. If one prefers vanilla, it would be ridiculous for them to demand that nobody should order strawberry.