I would say that... conflict happens. Constantly. It's a given. I've seen it not only online here at points, but also offline. In my first year of college I was in a D&D group where two of the players were a couple. They got mad over some sort of argument and basically used their in character time to berate each other's characters, leading to some awkward moments.
Honestly, if you think you'll never have a problem with another player, think again. As humans we like to constantly search for drama. It's just how we function as a society that lives in a very advanced urban setting. Someone is BOUND to tick someone else off, but with the internet the possibility of finding that one person that does something that ticks you off is infinitely higher.
Games mesh far better when everyone is on equal footing with everyone else. I've been in some great rps... and when people aren't happy with each other those circumstances can turn an rp sour. You can try and deny that you'll never use in character interactions to further a grudge with someone... but that's a lie. Deep down there is a bias in you, and thus that bias will develop in your characters. Such bias tends to spill out into creative work, and rping is as creative as it gets. We use our emotions to interact with the characters and setting, so anger can likewise be channeled.
IF you have a problem with anyone talk to them about it. Don't be intrusive, just say what they are doing that is bothering you and see if you two can reach a compromise. If you can't... well... you'll have to find other means of dealing with the situation.
As for a good relationship with the gm, that is very important. Remember, gms are people too. I've had D&D gms in the past that wrecked someone over just having a bad relationship with them. That single person would get ALL the traps thrown at them, or end up broke by the end of an adventure. Likewise online I've been to some websites where stuff like that is common. A gm who feels angry at a player and uses their power to make their experience horrible.
So, all in all, it's going to happen one day. You just have to know how to deal with it when the time comes.
