Honestly, yes. Even if people do know that plastic is bad for the environment, they honestly don't care. I might be comparing California oranges to British apples here, so forgive me if this doesn't match your experience but here's a quick summary of what I see.
Back in 2007 San Francisco enacted the beginnings of a City-wide plastic bag ban, banning them and charging 10¢ for paper bags. First at large retailers, then to all retailers by about 2013 IIRC, I might be off a little bit on the time frame.
Here's what happened: I went from seeing plastic bags littered in the streets every day, floating around in the wind, a sight that was incredibly common since as far back as my earliest memories as a kid to not seeing one single plastic bag left on the street in the past 4 or 5 years? Can it still happen? Sure, theoretically, but as the other cities and counties around here started enacting their own ordinances, the chances of that happening were sharply reduced. Now there's a State-wide law that's largely the same.
Now I've also worked in the service industry in the past, and when it comes to disposables, people are pretty liberal about their use. A café I worked at had a refill policy that lasted the whole day if you brought back your cup, but hardly anybody would bring their cup back and we would still give them the refund anyway, but the idea was that would be one less cup+lid to reuse. We would also subtract 10¢ from the price if someone brought their own cup, but still, hardly anyone does.
Even if people were planning to eat in the café, oftentimes they would request to go orders "just in case", which meant more paper/boxes/plastic utensils/whatever. Oh and if you provide those stupid little plastic covers to close up your plastic lid and prevent spilling? Just another crappy piece of plastic. Ice cream shop or cake shop? Expect to go through a lot of wax paper, unnecessarily most of the time, along with paper cups, and either wooden or plastic spoons, not to mention those wooden stirring sticks. Or if you don't make straws readily available, then most of the time, people won't even ask for one, but if you put them right there in front of them, then suddenly you're buying a lot more straws to replace them. All of this is just one-type of business in the city. Go to another place, suddenly you're dealing with disposable chopsticks, or little plastic salsa containers, or some other crap.
This is a city that is considered 1. pretty liberal and conscientious and 2. pretty environmentally friendly, but take a walk in any neighborhood and just note the trash on the ground. Cigarette butts (which incidentally the city charges a 75¢ fee per pack of cigarettes ostensibly to recoup costs from clean up, but is really probably just a double down on sin taxes), broken bottles, any kind of chip bag, bits of sandwich wrapping paper, paper cups from coffee, you name it, it's around. Just not carry-out bags, or if you do see those, it is pretty rare compared to 10 years ago.
Sometimes I wonder what would happen if you taxed/enforced an extra fee collection at the point-of-sale for all of this crap? Or just banned it all outright. It's worth thinking about because obviously people don't really care, and if they don't care here, they probably care even less elsewhere.
Either way, it'll be worth paying attention to what happens in Taiwan from here on out, and in Scotland when their plastic straw ban comes into effect.