In the MQ, I'm at the point where I need ti find Esbern. In the Civil War, I need to deliver Balgruuf's axe to Ulfric. Can I finish the war without negative consequence concerning the MQ? I've heard some people say it can cause issues.

My reasoning is this: I want the trophy for Dragonslayer to be my last trophy I need for platinum. I'm working on the Thieve's Guild now, which will finish my guild trophies. Then the Daedric quests and the Civil War and MQ trophies are all I need.

It shortens the main quest a bit. There's a meeting that gets eliminated because some of the participants are dead. If you want to experience it, you need to carry the MQ further.

Actually I think it's better to finish the civil war quests before doing the MQ, personally. If the civil war is ongoing, as noted above there's a part in the MQ where you need to negotiate a temporary truce, and that can get buggy. If the civil war is over, no need for the truce.

+1