When is a trainer allowed to switch pokemon?

Is it at any time during a battle? I don't think so, otherwise,
there is always the chance of an endless loop of switches.
For instance: If Trainer A sends out a fire pokemon while
Trainer B has a grass pokemon out, Trainer B immediatelly
switches with a water pokemon. Trainer A immediatelly
switches the fire pokemon he just sent out with an
electric one, Trainer B immediatelly switches with his grass
pokemon he had out in the first place, Trainer A sends
out the fire pokemon again etc

Usually, the referee says the rules of switching Pokemon. For example, in almost all Gym Battles, the referee says "only the challenger is allowed to substitute Pokemon" or something like that. However I think this doesn't apply in the Pokemon League battles.

So, when none of the two trainers is a gym leader, are they allowed
to switch whenever they feel like it? Is there always a chance that
they'll get into an endless loop of switches?

It looks like challengers and trainers battling can switch whenever they want. They've shown trainers switching Pokémon during a battle when they were about to be hit with an attack at least a few times.

Gym battles and Pokemon league battles.
On friendly battles will depend on what both trainers agree.

Nobody has really answered my question though.

During their Sinnoh League battle, Paul and Ash both switched pokémon numerous times in quick succession early on

Could be whenever there's a lull in the battle, or between "turns"