What fabric do I want? Is wool/polyester blend a thing?

I say you got a lousy polyester shirt if it’s pretty new. If it’s well-used, then yes, that happens to polyester.

If you use/wear it a LOT, like dozens of time, yes, it will gradually build up a smell that will become pronounced if you start sweating in it. Laundering it won’t 'get it out.

But new polyester shirts shouldn’t smell for a long time. Definitely not in your first 10 uses.