Is it OK to be picky about math you find interesting? I am a layman interested in mathematics, and I would like to hear mathematicians' views on the following: Is it normal to be picky about mathematical stuff you find interesting?

I ask because 80% of math I encounter does not seem interesting to me. I want to know if this is true for most people or if there is something wrong with me.
At any particular moment, or for stretches of time, it is entirely reasonable to find various things boring... or incomprehensible, or both.

But/and as one learns more, one's opinions will inevitably change.

And, yes, admittedly, many published papers are contrived, with the main goal of having a publication to make a good impression on dept heads, deans, and funding agencies. No real intrinsic interest... and it's hard to tell, from an amateur's or novice's viewpoint.

So I'd recommend that you (and everyone...) follow their own tastes and curiosity, BUT be open to the possibility that things that seem boring or pointless or incomprehensible at one moment may later seem quite otherwise. Don't pretend to make permanent decisions...
I would say it would be unwise and rather odd for a mathematician to dismiss any part of the subject matter of mathematics as uninteresting. The subject is very large and there are deep connections between apparently very different aspects: as a simple example, consider the many different proofs of the fundamental theorem of algebra. If 80% of the maths that you encounter seems to be uninteresting to you and you can't see why that 80% of interest to anyone else, then I don't think maths is for you. (I'm personally not very excited by the the theory of differential equations, but I know it's an important subject and I appreciate all the work that's been done on it over the centuries.)