The rules on Multiple Similar Magic items are :
Multiple Items of the Same Kind
Use common sense to determine whether more than one kind of a given
magic item can be worn. A character can't normally wear more than one
pair of footwear, one pair of gloves or gauntlets, one pair of
bracers, one suit of armor, one item of headwear, and one cloak. You
can make exceptions; a character might be able to wear a circlet under
a helmet, for example, or be able to layer two cloaks.
The Slippers of Spider Climb are described as light shoes (which could almost be imagined as socks), so would it be reasonable (under common sense, as above) to allow a character to wear them under bigger boots, like Boots of Speed, for instance ?
Best Answer
It's possible that the boots are roomy enough to accommodate the slippers (especially since they are size magic), but (using common sense) I suspect that the slippers may not function unless they contact the surface to be climbed. They seem to operate by grip given that they don't work on ice, etc.
If not "grip" by ordinary friction, it is by some interaction with the surface they are in contact with, (and they seem to grant the wearer some immunity to the effects of gravity), slippers in contact with the inside of the boots seem unlikely to allow the boots to walk on vertical and overhanging surfaces.
While wearing both reduces the time taken to change from running to climbing mode, it would not eliminate it, nor would it allow running on the ceiling. However it could be argued that the slippers grip the inside of the boots making it hard to remove the boots!