I find your comment though about museums storing coins on a square of clear perspex interesting. You would still get a lot of "slide" that way, though maybe the perspex is deemed softer than the plastic. I try to keep mine on felt squares and where I don't have enough I have them on the paper tags until I can get more felt.
Tags can be potentially abrasive. It depends. After all, one of the classic coin storage systems is 2x2 paper envelopes, so it's not paper as such that's a problem, but perhaps the nature of the paper/card. Some
types of felt can be abrasive, and some not. Natural felts can be scratchy. Wool felt is absolutely the worst, and can ruin a coin in months. Perhaps silk felt is better. The artificial felt used in Abafil trays seems to be
fine, at least from my decades of experience.
The squares of clear plastic used in museum systems are not very soft, in fact they are relatively stiff, but they are perfectly smooth and thus non-abrasive, and presumably also an absolutely coin-safe material: that means no plasticisers, which implies stiffness. The tags sit under the plastic. These systems have trays without compartments, full of small open boxes, the coins sit on plastic, on a tag, in each box. When you want to examine a coin, you remove its box including tags. This avoids disturbing the rest of the tray, and keeps the coin and tag together at all times. The loose boxes also allow the coins to be rearranged without having to touch a single coin.
Thinking further on the matter, although I expressed neutrality among several different storage methods in my prior post, I don't really feel neutral. My view is that open trays are better, in allowing air circulation, and drier conditions. Variations between humid days and cold nights means that moisture can potentially condense as water in a
flip, although this may be more a theoretical than real problem. Even for coin-safe
flips one has no absolute guarantees that there are zero chlorides, and one can make mistakes in the choices of
flips. Paper
flips instinctively feel safer, but who, apart from RBW (as those who buy
his duplicates will know) uses paper
flips nowadays? I also don't like the idea of plastic mechanically sandwiching my coin faces and pressing on the surfaces. Regardless of BD, or chlorides, who knows what the long term effect might be? I don't think it can do much for
toning or
patina. My open trays result in slow and lovely
toning. So, though I'm not claiming any higher level of technical wisdom on this, it's open trays for me, and I'm sticking with what I'm familiar with.