I actually wouldn't mind those, assuming they aren't the extremes I'm sure you intend to imply. A cowardly fighter would be fun, if their cowardice didn't prevent him from taking part in fights, but was, perhaps, specific to situations, and maybe caused him to simply avoid a kind of enemy, rather than not fighting at all.
The cleric could also be fun, so long as he wasn't a preachy SOB who told other people to do what he wants all the time.
The cowardice didn't stop him taking part in fights, and wasn't specific to one type on enemy - which I personally think makes a fun and interesting character quirk, like a barbarian who thinks nothing of throwing himself at a dragon but won't touch a spider. No, what made that annoying was the 5-15 minutes of arguing in-character we had to go through every time there was a possibility of a fight starting, since the player refused to have his character take part in the fight until they'd been persuaded in-character. Mind, the player was a bit of an attention whore in every game I played with him, and I think this particular way of making sure he get his spotlight time was not intended to be quite as annoying as it turned out.
As for the pacifist priest, the problem was simple. When he wasn't pusruing his particular quest, the character was going to retire to his grove (priest of Eldath in FR, for those who are familiar with the setting) to meditate and cleanse himself. And if the thing the other PCs were doing wasn't related to what he was reluctantly doing, then he wouldn't take part. So either the game session was about his character, or his character sat out the session. Which was unfair to other people if they had things they wanted their characters to do, since they didn't really want to exclude the player regularly but his character concept meant they had to. Or they could be sidekicks in his story, which also isn't exactly fair to them.