Don't know if going through this door will kind of ruin the main storyline for me, will it?

The main quest of Oblivion and Shivering Isles are in no way related. You can do them in any order you so choose. Although a reward from Shivering Isles can help you in a battle with the Oblivion main quest, it's not required by any means.

Nope, do anything in any order. The only consideration may be leveled items that you might want to collect later in the game. You can also travel between the two worldspaces whenever you wish, so they can be done in parallel. If you find you want an item from the other realm, go fetch it and come back.

There are those who would advise not finishing the Main Quest, and some don't even start it (using alternative start mods).