There is a fundamental difference between immutable traits, such as race, gender, sexuality, and physical ability, and political beliefs. So your comparison to "something you strongly disagree with" is not fitting analogy.
Your beliefs will of course outrage some people that have opposing ones, but they are yours and they should be protected no matter what they are or how wild or somber they are.
We aren't talking about "beliefs". We're talking about actions. Discrimination is an action.
It is only when you actively start harming people or directly denying human rights is when it becomes an issue…
And denying people goods and services based on who they are is harming them. So it is an issue.
You can’t make someone do things against their beliefs, just as you wouldn’t want to be made to do things against your own.
We can and we do, all the time. That's part of living in society.