I think actual conservation is ok. Light surface cleaning if the card is really filthy, deacidifying for stuff like strip cards that won't make it another 90 years without it, that sort of thing.
Removing stains etc is to me where the slippery slope begins.
Pressing/trimming/rebuilding etc shouldn't be acceptable. I can see some exceptions, but they'd need a lot of transparency and disclosure. Even then, it's just way too likely it gets cracked out and regraded without disclosure.
Here's an example of what I believe is ok. This card was in a small paper bag with a stack of other cards, It stuck out, and got partway coated with soot and grime. It must have been in there for decades. I removed some of the surface grime with just a q tip and water. That sort of grime would eventually cause long term problems.
It still has a bit of grime in the tiny cracks that sometimes happen in the surface coating over time. I probably could have gotten that out too, but I think that would be going too far, and I was way too lazy to spend a few hours doing that.
Before
After
