I use this all the time. It often happens on this site and in real life. After a while butting heads hurts and one needs to back off and admit there are differences.

So is it ok if I don’t agree to disagree?

A pretty basic skill/strategy, which most of us employ, often without even thinking about it.

A good deal of my professional work is very political, so this ability is practical (sometimes very challenging) and a lot of good work would go undone if we let valid disagreements stifle collaborative opportunities. I try to cultivate problem-solving relationships, as well as mutual respect (when possible), which allows for “agreeing to disagree” in the first place.

Actually, that's not as easy as you make it sound. I will not "agree to disagree" that where I was born, whom I choose to love, the color of my skin or which sexual organs I may have makes me a lessor person and deserved of lessor rights and privileges as a human being. That's just what I can think of off the top of my head.

Some things are simply wrong and agreeing to disagree allows some things to be considered an "academic discussion" and ignores that the propagation of some ideas actually harm people's lives.

I think you can keep your lessons. They don't seem all that relevant.

Most of my friends are Christians. We don't talk about religion. That's easy.

My sticking point is when a person's beliefs infringe on my rights, or the rights of minorities.

Then I fight back. VOTE!

I agree, until their beliefs influence my options and rights. Then it becomes my business too.

Ranchero

I agree to disagree already, it’s a policy I adopted a very long time ago. All my friends are believers in god and the only way to accommodate their beliefs and my disbelief is to agree to differ. We just don’t engage in the subject of religion and belief at all, and the problem of disagreement never arises.

This is my friend’s new truck