If you are using the app, I believe you can get rid of this under settings > username > enable home feed recommendations. Turning it off makes the app way more usable.
So it's been a week, and I haven't had to mute a random sub in all that time. Seriously, thank you—maybe it would be better for me to stop using Reddit, but if I'm going to be using it, at least it's not constantly throwing crap I don't care about in my face.