I believe all those who have joined a group RP have found themselves in at least one the has the issue you are dealing with. The first group RP I tried to join on here I got blasted into nothingness because there was so many 1x1 replies going on in the thread so I didn't even know what was going on because it was 20+ posts per day. So, I just told the GM I was out because I couldn't keep up.
Look for group RPs that use what I call a round robin system (based on MMORPG loot options, lol) where each round starts with a GM post and players can only post once per round; doesn't even need a post order. Additionally, look for group RPs that are not players breaking off into constant 1x1s which can overwhelm a thread fast when there are 6 players all posting 1x1s in the same thread. That isn't exactly what I would call a group RP if the group constantly is breaking off from each other.
The problem is going to be finding these RPs, so it's best to just ask at the get go. "How often do you expect players to post? Is there a posting order or a post round system? Are players in the groups allowed to wander into 1x1s in the group RP thread?" And so forth.
There is no standard appropriate reply period because each RP and GM is different in their expectations. You just have to find a roleplay and a GM that will work with you.
When I host RP's I typically make it so there's a post order. People can only post in the designated order, which means nobody can post until the person before them does. It usually works pretty well as it accommodates for different posting speeds.