Happened the other night on my last session: We were having the climactic fight in Cragmaw Castle, and the players had the brilliant idea to try and lure the owlbear into King Grol's room. So, while the owlbear was busy fighting their enemies, the rest of the party was camped out in the nearby storeroom. Then the monk decided to partcipate in killing the owlbear. Fine, sure,that works.
I wait for him to tell me what he was doing (as his mic and speakers weren't working so we could only talk to him through text), and he doesn't respond. So after a minute or so, I decide to skip him, only to receive a message: "sorry, I was looking up the stats for the owlbear."
I have no qualms with you taking advantage of what you know from past experience, you may even read the MM in your free time, but please don't be reading from the MM during the session. Fortunately I was able to just tell him that and we could continue on. At some point I may have to explain to them how that cuts into our gaming time and is frankly a little rude that you'll ignore the game to be trying to metagame a victory.
I would've replaced him when I found out he had broken mic and speakers. I don't go in for text play during a voice game. I've had a lot of folks try and pull that on Roll20 over the years. I kick them immediately.
To be fair it was more the roll20 client and his computer don't get along. He's usually *fine* in most other sessions. I'm trying to debug it for next session.
I guess I'm not fair then, haha. Too many years of online play have left me intolerant of PC issues. Kick-n-replace is my policy.
As to the real objection, I wouldn't care that the player is referencing the Monster Manual during play. I would care if that meant the player was unresponsive or slow to act. Read that thing off-turn!

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.