One of the players I play with said that it is not allowed by the rules that you drink more than one potion in one round, but he could not find the rule anymore.
There is no such rule that I can find, and I tend to think that I would have heard of it if it existed. It certainly isn’t to be found anywhere in the potion rules, which is where such a rule should be found.
And even if the rule existed, a mutagen is not technically a potion in any event, and wouldn’t interfere with that rule. The only way you could possibly be prevented from doing this is if the mutagen class feature said you could not drink a mutagen the same round you drink a potion. The mutagen class feature does not say any such thing, nor has any errata or FAQ for mutagens (that I have seen) said this.
Normally you could not do so just because of action limits, but Potion Glutton is one way around that. Note, however, that Potion Glutton only gets around the action limitation if you have at least one potion in hand—if you have to pull both potions out, you won’t be able to drink the second one (move to draw one, swift to drink it, standard→move to draw the other, out of actions). Unfortunately, the nerfed Pathfinder version of Quick Draw doesn’t help here, either.