Is there a specific name for the kind of shirts Charlie Harper wears? To me, they look a lot like bowling shirts, but I wouldn’t be surprised if there was some Californ-i-yay/Malibuey name for them. (I mean, if the shown had been set in Honolulu, he’d be wearing Hawaiian shirts, right? So what are these?)
A Camp shirt or Bowling shirt?
Kids wear shirts like that at summer camp? 
Whoops! Charlie just called them “bowling shirts.” Question answered, ignorance fought! 
Yeah, I’ve bought them on eBay using “bowling shirt” as my search.
Larry David wears them on Curb Your Enthusiasm, IIRC.
I know that this is a device to make Charlie look like a man-child, but would anyone in his social circle actually wear clothing like that?
I’ve called them bowling shirts, “regular guy” shirts (from the Rodney Dangerfield movie Easy Money), or Cosmo Kramer shirts.
He may be rich, but he ain’t exactly High Society. I think the closest they ever got to showing him with “friends” (other guys) was when he had that booze-and-cigars session with three famous dudes.
His social circle is hookers and drug dealers.
I’d wore them in the past, and I would now (though not all the time). I don’t know what that says about me.
I call them “lounge” shirts, after the lounge music revival as seen in Swingers.
They were retro cool in the 90’s.
In a few of my chorus’ concerts, we had to wear these, in a variety of solid bright colors, over black t-shirts. We called them camp shirts.