Is it possible to switch the button behavior? Certainly you can do it in the OS (mouse settings for left-handed folks), but I wonder if there is some kind of plug-in specifically for Blender?

Yes, no plugin required. In fact, because this appears to be such a showstopping issue for many users, the option is right there on the Blender splash screen: there is an "Interaction" dropdown that can be set to "3dsmax" or "Maya".

You can choose whether you select with the left or right mouse button, if that's what people are talking about with the "inversion": https://www.blender.org/manual/preferences/input.html

So much Vim in that the letter keys start doing random crap instead of, you know, typing?

Some bad UX decisions get baked in and you have to live with them, though the nice thing is Blender can be switched to operate in completely different flavors. There's one that matches what Maya does quite closely for those who prefer that.

Check your User Preferences options. It's extremely configurable.

Yes I would say that old users Know how to configure settings or already set them and new ones can be confused by defaults. But that's not so complex after all. I'm very grateful for such a superb software.

To me this doesn't matter. I mainly use the keyboard for most things anyway.

Blender's UI isn't intuitive, but it is fast and quite efficient.

Blender has keyboard shortcuts for everything. Learning these is a beast, there's just so many, but once you do things get a lot faster.