Can you touch the tubes?

You’re thinking of those awful halogen lamp bulbs popular in the 80s. Tubes are perfectly fine with skin oils on them. They really don’t care. You’re actually far more likely to damage tubes from them slipping through some silly cotton gloves.

You’re pushing/pulling those tubes in/out of their socket-that’s done by the base of the tube.

Vacuum tubes powered WWI/WWII. There wasn’t concern for MIC white gloves and heeding goofy audiophool "rules".

Touch the glass if you must- no one is looking.

If a tube has a separate base, you pull and push it in by that base to prevent separation of the base from the glass envelope.  But there is NO need to be concerned about oil being deposited on the glass.  That concern comes from what happens to some types of light bulbs.  Oil deposited on the glass of such bulbs carbonizes from the intense heat.  That black spot will absorb light from the bulb, rather than letting the light pass through, and this causes that spot to heat up so much that the glass fails, which causes it to explode.  This kind of heat an light production never occurs with audio tubes.

Bulbs that run very hot like halogen bulbs need to be kept free of oils.  tubes, not so hot.  use your fingers and don't drop them.

For some amps it's difficult to use the base of a tube to push and pull into socket. I found if I just grip it comfortably around the upper portion of the tube and rock it back-and-forth while applying pressure as it slides in.  Of course there's always a fear the glass will shatter but I spread the distribution of my fingers which I think reduces the risk.

If you try to squeeze an egg in your hand with a lot of pressure it won't break but if you start angling your fingers into the egg it will break. I'm not gonna try this with a tube.

if The tube shatters who knows what happens at that point aside from losing 50 to 100 bucks on the tube and debris field.