The problem here is that treating politics as 'just politics' is the realm of people privileged enough that they have never directly suffered because of those politics.
Transgender rights, for example, are never 'just politics' for me: they are a basic moral issue that deeply affects the life of one of my close friends.
I believe the fundamental dichotomy is that, for some of us, our opinions are not who we are. We can change our opinions and remain the same people.
For others, their opinions ARE who they are. They cannot separate out their beliefs from themselves, so when you question their opinions, they feel you are attacking them personally.
And in that case you cannot respect those opinions?
Look at gay marriage. There are large percentages of people in the US who would like to return to a time when gay marriage was illegal. If you were married to a same sex spouse, do you think you'd be able to say "oh, that's OK, I respect your difference of opinion." No, you'd do everything in your power to protect your family from being attacked.
I mean, just imagine how straight people would react if the government tried to invalidate their marriages.
I thought the parent comment suggested that the opinions of those who cannot separate out their beliefs from themselves, so when you question their opinions, they feel you are attacking them personally, are less respectable.
At some point you need to draw a line.
This is hard and may backfire in a deeply divided country. To me, instead of trying to achieve a common ground (which, in the current situation often means forcing 49% to the position of the 51%; with the chance of a swap in 2-4 years) we should learn to live, share space and collaborate with folks who hold different political views.
We can disagree on politics, but it should not prevent us from working as a team on software or sharing a beer after work. We are not at war with the other half of the country. We should respect their opinions and avoid unnecessary confrontations. My 2c.