Evil is all a matter of perspective. As for as the whole daedra not being evil I look at it this way, while human beings aren't evil by nature, some humans are seen as evil by others due to their actions casing harm to others(ie. Hitler, Stalin, and the man in charge of the terrorists responsible for 9/11 who's name I'm not even going to attempt to spell). Same can apply to the Daedra, the majority of them have negative interactions with mortals that usually lead to large numbers of people to be hurt or killed. This leaves the mortals to view these daedric princes as evil. As a result most people avoid interaction with these princes and despise anyone who does interact with them.
To puggles, If I remember correctly,Most daedric quests start out as Misc. objectives that can be avoided simply by never following up on them, for example just don't visit the shrine of Azura or Boethiah, of your character is anti daedra why would they ever do that anyway unless to try and convert the followers? When you come a cross Meridia's beacon then don't pick it up. You can pretend that your character did pick it up but dropped it as soon as Meridia started talking to them.
I think there are only two or so quests that are imposable to avoid starting in their entirety. Clavicus Vile's quest triggers itself when entering falkreth at a certain level. While you can basically ignore Lod's and the guard's dialogue regarding a lost dog, You'll still come a crossed Barbus who will talk to you and put the quest in full swing, eventually. Though I think there might be an duologue option to tell him to leave you alone so he doesn't become a follower and your not stuck with him.
The second quest is Hermaeus Mora which will start during the progression of the main quest line. While I have no idea how to avoid it, save simply not complete the objectives, ie don't harvest the blood, and if you do don't turn in the quest, you'll be stuck with the quest items. Of course from a roleplaying perspective your character wouldn't know that Hermaeus Mora was involved until he showed up at the end of the quest anyway. That is what I decided with my mage who is almost anti-deadric. Normally he wouldn't want anything to do with Hermaeus Mora seeing as Hermaeus tends to kill people he's taken information from, but he didn't know Hermaeus was involved until after so there was nothing stopping him from completing the quest.