Is changing tempo during the song and back again a common device used
on modern popular music? Or is there a good reason to avoid this type
No, it is not a device commonly used in popular music. However, this technique is extremely common in other forms of music. There are no good reasons to avoid this technique, band musicians are still musicians. If a clarinetist can change tempo in an orchestra, a guitarist can change tempo in a song.
Does it pose any particular problems for either the listener or the
musicians who must play the song?
For the listener, they are a little confused at first (depending on the nature of the tempo shift) but unless you're doing it every two beats, which could be a little disorientating, the confusion quickly subsides as the listener then adds temporal shifts to their aural vocabulary about the piece. The next time you do it, it'll make sense to them.
For the musicians, really the only problem is making sure you all move at the same time, the same speed, and arrive at the same tempo. If you don't read music, learning and incorporating this technique will be more challenging, but you should all be able to do it just fine. I would start by practicing going between double time and half time and move on from there.
Assuming the negatives aren't prohibitive - are there certain
guidelines that should be adhered to in an effort to make this type
change more effective or less disruptive (ie. try to use a multiple of
2 on your Bpm)?
Who cares about disruptive? Make your music interesting; if it's disruptive for them, that's their problem, not yours. As I said, I would practice double time -> half time, and then try different modulations. I would try (as a band) starting slow and then gradually playing faster, and then doing the reverse. I would purchase a metronome so you can all practice agreeing on tempi. I would also work out some sort of visual signal from whomever is the "leader" to everybody else so that you know when to start / stop speeding up or slowing down.
If you're doing really complicated temporal modulations, I'd recommend click-tracks you can place in your ears. Many 21st century musicians who play very complicated music use click-tracks to help make sure they play the rhythms correctly, stay in tempo, and not get lost.