question about polyquat stains and cotton t-shirts

I posted a pic here before of a shirt stained from the washer and you guys helped me identify the problem as polyquat spots, which was really eye opening because it made me remember a few times in the past when my clothes got similar stains. When I was younger my mom used fabric softener in the wash and never cleaned the machine. Every now and then, seemingly just randomly, sometimes months or years apart my cotton t-shirts would come out covered with those dark spots. I did learn at the time that this was most likely caused by fabric softener residue in the machine; what I didn't know then, but do know now thanks to your help, is that fabric softener itself contains polyquat! (how convenient for the companies selling all these laundry cleaning products)

I am staying abroad in an airbnb and while at first I thought it was just that one shirt (which got a TON of spots) was the issue. I didn't even think to look more closely at other shirts. But then another came out with a spot or two, then another. Then I began to examine all of them under bright light and found the spots on them all. Sometimes it was just a few, sometimes maybe just one or two. Long story short: now all my cotton t shirts (newly purchased just weeks ago) have some amount of the spots. I've stopped using the washing machine in the airbnb. Just not worth the risk of more spoilt clothes.

But here's the thing I've noticed and that I'm curious about: it's only my cotton t shirts that seem to get the polyquat spots. I remember this being the case with the fabric softener staining I mentioned earlier, as well. It was always only cotton t shirts I found spots on then, and it's the same now. I have a lot of linen or linen blend clothing. I don't know if I just haven't looked cosely enough at it (sometimes the spots are small and if the fabric is colored one might not notice them unless looking for them) but so far as I can see none of that clothing has picked up the polyquat spots. It's just my cotton t shirts that are getting ruined.

And to be honest I can't even figure that out, because one t shirt might come out of a load of laundry with no spots, another with one or two, another with a whole range of them. It just seems very random and unpredictable. And meanwhile linen items laundered in the asme load look fine.

Why would this be Are cotton t-shirts particularly prone to picking up these residues for some reason