Is it best advised for the sake of convenience to stick with the same BPM throughout the entirety of a song or is it common and accepted to have multiple different BPMs in the same song?

I'm curious as to how this is viewed upon. Is it best to just write everything based around a set BPM?
Sometimes it's easier to have one BPM, but as long as the tempo change fits, there's no rules saying you can't do it.
Most recordings are likely the same tempo all the way through, recorded to a click. Without a click, there's a give and take with the tempo, such as if you're kicking it into a double-time or half-time beat.

The only time it would be a serious obstacle is if you've got a software track that can't be adjusted partway through (ex a GarageBand loop). But you can still set an external metronome to a different tempo and perform parts.

Really, just try to capture what the song needs.
It can be very effective if used correctly, really taking the listener by surprise, but it's also fairly easy for it to sound out of place.
It's a bit weird when, for instance, a verse and a chorus have different BPMs, but often a different tempo in a bridge or intro section is nice (compared to the rest of the song). Also check Dead Kennedys "California uber alles", it changes BPM a lot of times through the song.
You probably wouldn't hear it if a chorus was 5 or 10bpm faster, but it can feel like a good energy kick, sometimes.
There are also plenty of songs out the@e that feature sections or movements at different tempos. The@e is nothing wrong with this if it sounds ok, although it can cause minor issues if you are working with computers on a grid. Most daws will handle tempo changes with a bit of extra fiddling though so don't let that stop you.