Is Supporting The Rights Of Muslims Hypocrisy?

I'm a part of several politically oriented groups on Facebook and recently this meme below showed up on my feed by a conservative showing an apparent hypocrisy in what Democrats do:

The thing is, you can support someone's civil rights even without agreeing with them on their political and social attitudes. Anyone who knows me or has read my blog knows I'm one of the biggest critics of Islam there is. I detest almost everything about Islam. But I will respect and stand up for the rights and civil liberties of Muslims to not be unfairly discriminated against and mistreated.

What does "Dixon Diaz" think Democrats should do? Fight for the removal of civil liberties from Muslim people in the US because we may disagree with them on certain things? Think of it this way. Should I, as a Democrat, stand up for the rights of Republicans to not be discriminated against even though I vehemently oppose their views? I'm sure every Republican would say "yes." In fact, many Republicans are complaining now that Democrats and liberals aren't standing up for the free speech of Republicans, particularly on college campuses. So there you go.

Now it's one thing to support someone's civil rights, it's another thing to support their agenda. I'm against supporting the agenda of Muslims who do not agree with the very civil rights I'd protect, who instead support regressive laws and policies. But I still think they deserve basic civil liberties. Liberals just need to be fully aware of this distinction, and so do conservatives like the guy who made this meme. Supporting someone's civil rights does not entail you support their views. And without doing this, no one would have any rights.