Would a libertarian society break down in 'Me-first-ism'?

Would a libertarian society break down in 'Me-first-ism'?

One of the favorite anti-liberty arguments (besides the "warlord excuse" or the "government invented the internet" myth) is the claim that without government holding a gun to my head, self-interest will cause civilization to crumble.

To all those who claim that a society based upon libertarian or even anarchist principles will fail before it even has a chance, due to "everyone for himself" being the rule, I offer some observations.

You are not likely to find a more "libertarian" or "anarchistic" person than me. Yet, I am the one in the group who actually tries to consider other people while the non-libertarians with me have a "me first" attitude in almost every situation.

Even if there were no "handicapped parking" spaces, I would leave the nearest spaces for those who need them. I don't need them, and for that I am glad. Some non-libertarians I know try to manipulate the system to their advantage so they can "legally" park there regardless of actual need. Or, they simply claim they "won't be long". I'd be ashamed.

In traffic I am always trying to make room for the person who is trying to change lanes. Many (most?) non-libertarians I have ridden with act like they must "win" and not allow anyone to be in front of them on the road. There is nowhere I need to be badly enough right now to drive like that.

I am more likely to judge the situation, not the person. Not that I am perfect in this, but I am able to see when I mess up. The authoritarian "alternative" is obvious and tragic, and composes much of the "news".

There are many other examples that I could relate, but the evidence which I see with my own eyes is overwhelming. A libertarian society would be a polite society for a variety of reasons.
I understand that being considerate is in my best interest. Maybe not in the short term, but definitely in the long term. Plus, it makes me feel better.
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What is it about Albuquerque and body parts? First it was the dismembered giraffe in the dumpster, and now this. While dead people don't care about what you do with their remains, their relatives do. Do what you agree to do.