I'm making the assumption that, without other information Gruumsh is run as designed. From Volo's Guide:
Gruumsh, “He Who Watches”
Gruumsh, the undisputed ruler of the orc pantheon, pushes his children to increase their numbers so they may be his instrument of revenge against the realms of elves, humans, and dwarves. In order to spite the gods who spurned him, Gruumsh leads his orcs on a mission of ceaseless slaughter, fueled by an unending rage that seeks to lay waste to the civilized world and revel in its anguish.
Orcs are naturally chaotic and unorganized, acting on their emotions and instincts rather than out of reason and logic. Only certain charismatic orcs, those who have been directly touched by the will and might of Gruumsh, have the capacity to control the other orcs in a tribe.
The bolded part is there because some people have said that maybe this cleric is really just worshiping Gruumsh as some kind of fertility god. They ignore the second part
so they may be his instrument of revenge. The only reason orcs are pushed to procreate is so that the offspring can go out and slaughter the other races.
Others have suggested changing the nature of the gods, or (presumably) the nature of orcs. There's also a bunch of lore in various books about how Gruumsh has a particular hatred of Corellon, god of the elves.
Then there's the description of clerics
Clerics are intermediaries between the mortal world and the distant planes of the gods. As varied as the gods they serve, clerics strive to embody the handiwork of their deities.
So a cleric of Gruumsh is not just someone going through a grunge phase. According to the PHB,
clerics strive to embody the handiwork of their deities.
I don't see how you can reconcile someone who wants to embody the handiwork of their deity who's sole mission is ceaseless slaughter of elves, humans and dwarves unless you're playing an all "monstrous" race campaign.
In a campaign where mixed races are the assumption and those races are going to include elves, humans and dwarves, running a cleric of Gruumsh is divisive.
None of that matters of course if this is just a light RP game where the god you worship is just a label that has no real impact. Or if it's been decided that the Gruumsh isn't really as evil as depicted by the books.
One last thing. There's a huge difference between the distrust between Legolas and Gimli and someone joining your group who says "Oh, by the way I'm the acolyte of a murderous sociopath. I'm a firm believer in killing you, your loved ones and your children when we get the chance."