Can you touch the tubes?

If a base is loose, even completely free of the glass envelope, as long as the wires are not cut, you can glue the base and glass together.  I use high temperature epoxy, but I have no idea if that is the best glue to use.

It is not that common for the base to come loose unless a tube is really old.  I run 70-80 year old tubes so I am careful.  Some not so old Western Electric 300B reissues had weak glue joints so care is needed.

I have never heard of anyone squeezing or pinching a tube so hard as to shatter the glass, but I suppose that is possible.  Aside from dropping a tube, the most common accident is inserting a tube incorrectly so that the pins are in the wrong holes.  That can happen if the key on the central post, or the post itself is broken off so thar a tube can be inserted even when incorrectly oriented.  Some 4-pin tubes, like 300Bs, don’t even have a key and rely on two of the pins being fatter; unfortunately, they are not fat enough that they cannot be shoved into the small hole of most tube bases so that a horrible accident is possible. 

Touching tube with bare hands is fine and no danger to health. Many folks do that.

I avoid touching the print, lettering/numbers, info on old 1950s-1960s 9 pin signal tubes. The oil from fingers can smear the print on the glass.

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If you look through tube manuals under Installation and Application the only things stated are the socket pin counts and whether or not the tube can be mounted in any position. Since "touching the glass" is not stated (or "do not touch if they glow") you can assume it's something too obvious to print. 

Tubes do not get hot enough for the oils on your fingers to effect them.

This partially stems from the halogen lamp (and others) days as those things get white hot.