How do you handle characters of different aligments in the same group?

Imagine you have a Cleric and a Rogue in the same group. The Cleric is a holy man and the rogue is a bit of a scoundrel.

My players would like to roleplay correctly, which would also mean that the Cleric and the Rogue would have to be in a constant conflict, escalating to many arguments and possibly ending in a combat or the Cleric leaving the party.

This is no fun and my players already have problems keeping the in-game conflicts in the game (like one player getting mad at another player because of what their characters did), so the Cleric kinda decided to look the other way/not comment every time the rogue starts acting roguelishly. However, this breaks the character for the Cleric's player, resulting in loss of immersion in the game and therefore lowering the enjoyment. So also not good.

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Are there any elegant solutions to this?