Those who oppose the teachings of the Church tend to do so because the teaching of the Church interfere with the notion that, "I can do whatever the hell I want . . . so long as I don't hurt anybody . . . anybody important I mean . . . and by important, I mean by my own standards, not yours . . . just @#$& off and quit imposing your views on me!"
Of course, the problem is "important by my own standards" is a vague, subjective term that, if accepted, means that someone else can decide that you are not important by their standards, and suddenly you're crammed in a boxcar or a gulag if they gain power over you.
But that's the problem with relativism. if values are relative to the person who applies the standard, and nobody has the right to judge another person's values, then to condemn another person for doing something we dislike is "judgmental," because he or she isn't hurting anybody important . . . by their own standards.
When it comes down to it, relativism isn't very freeing at all. it's used to justify MY freedom from YOU, but not YOUR freedom from ME. . .
That's basically a case of "might makes right." If you have the power (physical, financial, political) to impose your will, you can do what you want. If you don't, you're out of luck until the wheel spins and you're on top.
History is full of examples of people in power rejecting objective values which conflict with their own standards. The results tend to show up in history books described in terms of disgust and horror.
So, what's the alternative? The alternative is the acknowledgement that objective good and evil acts exist, where one is to do the former and avoid the latter. If we think Nazism or Racism or other things are wrong, we need to look at what makes them wrong in comparison to similar actions, and then make sure that we avoid the thing that makes them wrong. Otherwise, you get ridiculous situations like, "I'm not acting like a Nazi? Do you see me mistreating JEWS? I'm only mistreating DISSIDENTS!"
In other words, objective morality tells us that it is not the fact that the Nazis mistreated Jews that made it wrong (but that it would be OK to treat others that way) but the fact that the action mistreated the Jews that made it wrong. If the Nazis' treatment of the Jews was wrong, it stands to reason that treating others in the same way must also be condemned.
That's an objective value--don't mistreat people. Of course then we have to make distinctions. Is incarcerating a felon "mistreating" him? If not, how do we distinguish the proper treatment from the mistreatment? When is the use of force just and when is it unjust? But the fact that there are many considerations does not change the fact that there are right ways and wrong ways to handle a case.
If we depend on relativism, only the person who decides can choose what is just and unjust. In such a case, we can only coax and persuade the person to change to how we would like them to behave--or use force. But if we recognize the existence of objective truth, we can appeal to justice and right and show the individual that what they are doing is wrong, even if it seems right to them.
That's basically why objective truth and objective morality defend freedom, while relativism actually endangers it.