To rehinge or not to rehinge a mint hinged stamp?

I think it is really a matter of personal choice. If the stamp has some value, disturbing the gum even more with another hinge may not we ideal. Also, great care needs be taken if you are going to remove the old hinge as this is an easy to create "thins" in the stamp which can quickly decrease value to point of creating a 'filler'

i now use Showgard mounts for most everything. If I have a MH stamp that still has the hinge on it, depending on how the hinge itself looks I may slowly pull it off, but if it resists then I will cut the 'flap' off using a single edge razor blade with a layer or two of scotch tape covering one end of the blade portion so the razor blade is less likely to dig into the stamp it self - sort of like a height guide that's about equal to the thickness of the stamp (sans hinge)  If this doesn't make any sense I can take a photo and post

If the stamp is un-gummed or otherwise used, I will soak any hinge remnants off (assuming the ink on the stamp is safe to soak)

It all depends upon the condition and value of the stamp. High dollar stamps get a mount. Low dollar items depend upon the condition, if the hinge is easily removed or only has a small remnant, they will get a mount. If there's enough of the old hinge left, they will get rehinged over the old one.
I also mark my album pages for the hinged stamps, so that I can easily tell and will replace them when a better copy comes around.

I use Vario stock pages in part to avoid having to add any potential future damage to the stamps in my collection by re-hinging them on album pages. Especially given the poorer peelability of hinges today, I would rather not contribute to any potential damage to the stamps from the next generations of collectors who end up with the stamps I currently own.