This may seem like splitting hairs, but I honestly don't think it is:
Military and police are groups that defend/protect their country, it's laws and it's fundamental principles, which they most likely support. Just like your previous argument: Police can defend and support the right to protest, without supporting the content of the protest. This extends to pretty much anything.
Doctors and lawyers can support a universal right to life, good health, and a just trial, and by supporting those things, it makes sense to help, defend and protect a patient / client regardless of their background, practices or actions.
In both cases, we could make an exemption for police / military / doctors / lawyers that are there just for the cash. At that point, it's basically, "I'm defending / protecting because I support me getting paid." and the whole argument is kind of moot.