...Any sleeve you wear will likely have nylon in it....
Sweatshirts are commonly cotton, or or fleece (most commonly cotton with polyester) with a good cotton content. Even at 50/50 the "melting onto your skin" thing is not an issue with chips. Heck, it's not an issue with welding spatter and slag. Of course it can "burn through" if you try hard enough, but unless you're actually trying to use a hand held propane torch to heat shrink the shirt to your arm, it's not an issue. Hot chips WILL stick to the shirt on occasion if they're good and hot, AND, kind of a "medium size", heavy enough to hold heat, light enough not to have much gravity to fall back off the shirt...). But burn through? Yeah, you can make holes if you try, but it doesn't stick to skin or hairs. Your arm will tell you it's time to move away long before you have an issue.
I just went and looked, and I can say that the sweatshirt I relegated to a beater ten or more years ago, that I have living in the workshop- That one is 80 percent cotton. The ones I wear as "standard" for work, they're two brands, (Thinner ones from Haynes, thicker ones from Guilden) one is 50/50, the other is 55/45. Neither one is a "melting" issue, and neither one is a "catching fire" issue, although the work ones are clearly less durable.
Wait, what?
None of the shirts or T Shirts I wear have plastics in; all are cotton. Where in God's name are you buying your clothes from?
Over here, mostly because of market forces (cheap......), one has to seek out "all cotton" if you want it in casual clothes. Everything that's readily available, anything that comes up first in a search, and anything cheap enough for brick and mortar retailers to stock it is a blend to some degree. Heck, they're even blue jeans and cotton duck work britches are showing up with "blends" in 'em. It's absolutely something that we've got to pay attention to when choosing work wear over here.
A 17" lathe with 8 hp will kill you before it slows a beat, so my hands stay on the handwheels and controls until I stop the spindle.
Quick story, something I got from my grandfather. He was a farmer, he literally cut the trees to build the house and barns by himself. And pulled the stumps out with horses. And built his retirement home the same way. Big old woodworking machines, the first of which (long gone by the time I came around) were flat belt driven from a stationary engine on a skid. By the time I came around the "big" stuff was gone, and the collection was reduced to a table saw, radial saw, planer, joiner from Craftsman, sixties and seventies vintage. And some big old bed sander.
Anyhow, his philosiphy was always to make the tools work for you. If it'll do it, it'll do it. If it's not how it's meant to be used, be careful. That was it. The ONLY time he'd raise his voice and intervene is if you broke his one hard and fast rule- Give BOTH hands something to do, because the empty hand is going to get cut off. Even if it was as simple as cutting a small piece on a table saw, where there's not room for two hands, this one took me some life experience long after he was gone before it sank in. Take that unused hand, and hold the corner of the table saw table with the other hand. Hold it tight, don't let that table move. Really? It's not gonna move, it's bolted down???? He wouldn't even let me hold that empty hand behind my back. No dice. That hand needs a JOB. That's hard for a ten year old to swallow, but in the end, it is absolutely an idle job for an idle hand, but that lesson (after some life experience and a few near misses) has served me well.