Yes and no.
These are almost never recycled and in a lot of places they are burned, not buried so they do emit CO2.
Unfortunately in Europe they replaced them with pfas coated paper which is worse for health and pollution (forever plastic)
In actuality, consumers have little to no choice in the products they use. I couldn't live a plastic-free life even if I tried, and I'm somewhat well off. When you have to shop at Walmart to make it, your influence is even less.
It's a strategy in responsibility shifting. Rationally, the source of pollution does not lie in the single mother eating with her family at Waffle House and using a plastic straw.
The Pacific garbage patch is mostly from fishing nets, and the other sources of plastic pollution are mainly from riverside cities too poor to have good waste management.
The whole plastic straw scare is so obviously attacking a minor non-issue at significant personal inconvenience, that I wouldn't be surprised if it was planted by climate deniers to make people angry at or cynical about actual environmentalism.
I agree with the latter, and I suppose I indirectly contribute to it as a society.
That being said, if you're reading this comment, you very likely in the top 20% of carbon emitters globally, so don't get all smug about it.