I specifically go to a yoga class because the instructor has knee problems so he never does kneeling poses. I hate when there's a sub who inevitably makes us do tons and tons of low lunges and balancing table.
I was going to come down on the side of Pilates mags being for Pilates. Until you said all you were doing was meditating. For that, use whatever you want. It is harder to balance on a plush mat but that's really not an issue in a meditation class.
Yoga is totally the wrong place for shaming of any kind. That's so wrong. Also I'm a fairly serious yogini and I have a pretty plush Jade mat (5/16") because it cushions my old lady knees and I like the balance challenge. If I am really struggling with a balancing pose, I can always stand on the studio floor.
I go to a yoga class that was created for me!! The owner of the studio had been my personal trainer and I was having knee issues. She had the yoga instructor do a class geared towards my issues!! I love it!