I want to create a new character. It should be a Knight character, but Im not sure how his background story should look like.

Basically I want him to be very interested in Tamriels Lore and worshipping the Nine Divines. I thought about making him a Crusader. As a Breton he is very intelligent and knows a lot about the lore, about the creation of Mundus and the Aedra and Daedra.

His aim is to protect as many people as possible. He kind of wants to be a executioner for the Nine Divines. Since they are Aedra and they stand for Stasis they don't really interact with the world and don't change things. My char wants to do this for them. He sees himself as blessed for being able to interact with the world and wants to use this ability to help as many people as possible in the name of the Nine Divines.

Now to the Daedra. I dont know much about the relation Aedra to Daedra. I know the difference but not how they accept each other. Is it possible for a worshipper of the Nine Divines to interact friendly with Daedra? On the one hand I don't think so, because Daedra stand for change and Aedra for Stasis. Aedra created Nirn and the Daedra didn't care about it. The Nine Divines sacrificed a lot to create Nirn while the Daedra refused to help.
But on the other hand the Daedra have similar powers to the Aedra and other than the Aedra, the Daedra really use it and interact with the world if they are able to. So the Daedra could be able to give my character the power to be strong enough to protect the people of Tamriel in the name of the Nine Divines. But would my character use it? Or is this Betrayal?

I think Aedra and Daedra are the antithesis of each other, and when allied strongly to one, they would not approach the other. Even if Aedra and Daedra don't have that kind of relationship, the character should, because he's only human, and perhaps cannot understand things fully, and thus acts the way he feels is right.

My inclination would be no, don't use it. That would be the right way, but if your character justifies it to himself somehow, then sure go ahead. But the proper answer would be no.

I've personally always considered the Daedra and Aedra to be, if not opposing forces then at least opposites in a way. In Oblivion, for example, the worshippers of the Nine Divines (of which Akatosh, Arkay, Dibella, Julianos, Kynareth, Mara, Stendarr and Zenithar are Aedra) seem to regard the worshipping of Daedra to be pagan / evil, at least based on how they talk about them ("I understand Daedra worship has become increasingly popular in the provinces..." etc).

So in short, I highly doubt a Knight-type of character who worships the Nine Divines would approve of Daedra worship and/or friendly interaction with the Daedra.

I see no problem at all with a follower of the Nine also showing tolerance for Daedra, if not accepting them outright. In many religions opposing forces act in concert, creating a balance between the two that is necessary for all existence. As you pointed out, the Aedra represent stasis. There can be no life with total stasis. Nothing can be born, nothing can grow, nothing can die. Likewise there can be no world with total chaos, as nothing can exist in the first place. It is only the interaction of the two that makes the world possible. The Aedra's gift to Mundus was stability, and Lorkhan's was the possibility of change. Without both, the world could not exist.

If you want a more mundane example, look at men and women. The total antithesis of one another. But somehow men and women have always managed to coexist, even if not equally. Or if you would like a more scientific view, take our Sun. There are two opposing forces at work in within it. One is that of expansion, caused by the nuclear furnace in its center that is converting hydrogen into helium and releasing tremendous amounts of energy in the process. The other force is contraction, created by gravity. This pulls the atoms of the sun toward the center, preventing its bits from just flying off into space. These two forces - expansion and contraction - are perfectly balanced, and because of that the sun does not collapse upon itself and be destroyed, or fly apart and be destroyed. Two opposing forces acting in harmony. Ideally the Aedra and Daedra act the same way on Mundus, and there is only a problem when one upsets the balance, such as Mehrunes Dagon trying to destroy the world.

Then again, I think Selena was talking about creating a basic follower of the Nine Divines, not an "out of the box"-thinker. In Oblivion, a basic follower of the Nine doesn't seem to tolerate Daedra worship, so probably won't be on friendly terms with Daedra themselves either. Of course, if you absolutely want to mix Aedra and Daedra worship, arguments like this one are completely viable as justifications for that. But typically, I think a Nine Divines follower wouldn't do Daedra quests.

No one is arguing that Aedra and Daedra can't coexist, it's just that a follower of one of them wouldn't seek the help of the opposing faction. Most Daedra worshippers have distaste for the Nine. Their also branded outcasts, and live in the wilderness. It's unorthodox to most people who follow the Nine. The nine are generally more accepted. You can't not believe in one or the other, as there is apparent proof of the existence of both. It's just which one you prefer to follow, or believe is right.

I believe in Cromm, steel, power & might. And steel again. Nothing else.

Nothing is black and white. Certain Daedra like Azura and Meridia seem to oppose evil creatures like Vampires, and their quests involve destroying evil. It could be argued that a Crusader who is open minded and dedicated to doing good deeds could consult with these beings, especially one of an Altmer or Dunmer background where interactions with Daedra are more common.

But if said Crusader is also a worshipper of the Nine Divines and wants to act as "an executioner for the Nine Divines";

I think this sounds like pretty intense worship of the Nine Divines, hereby making the Crusader pretty much a fanatic. Fanatics have the trait of closing their eyes to pretty much everything other than their own personal beliefs/moral standings, making an open-minded executioner for the Nine Divines pretty unlikely, in my opinion. No one said Daedra are evil, but the basic nature of Nine Divines worshippers tends to be of the belief that the Daedra aren't to be associated with. Daedra worshippers are outcasts, whereas the Nine Divines seems to be the way to go in Oblivion. Even though the Aedra and Daedra aren't good and evil, the way religious people in Cyrodiil percieve them is quite black and white.

Then again, if said Crusader had started out as a Daedra worshipper and later on also included Aedra in his beliefs, I think the idea of him/her associating with both seems a lot more reasonable. Aedra worshippers tend to think Daedra worshippers are evil and therefore should be shunned, and Daedra worshippers seem to think Aedra worshippers too goody-two-shoes and isolate themselves willingly. If a Daedra worshipper were to decide to also like Aedra, he/she could realistically be of both sides. I think it's more unlikely for someone who starts out fanatically involved in Aedra worship to start dabbling in Daedra worship, though it is possible, of course. In this second scenario, the Aedra worshipper "turned bad" would probably keep his/her Daedra worship a secret, though, and not openly admit to also following Daedra.

In Oblivion I allways found that the nine were considered better than the daedra.
Not going into lore too much this is shown in game by the shrines and their followers being shunned and hermits in nature, and those that know of their existence scholars, mages, heathens and woodsmen / scouts.
In lore this is imo more to do with the empire stamping its identity firmly on all it conquers including the following of the nine.

That said the daedra mostly are not shown as evil most of the time just capricous in nature, so there is nothing stopping your character from worship of all forms in Oblivion.

Then maybe doing those quests isn't for him.

But what if he happens to do something in the name of the Divines that Azura or Meridia would have wanted him to do? What if he only grudgingly accepts the quests in order to purify the creation of the Aedra? You could find ways to make this fit his personality.

Well, like I said earlier, you can always find ways of justifying a character's actions to suit what you want him/her to do, but in the end it comes down to what's more likely/reailstic. You can have a fanatic Nine Divines worshipper also be open-minded and like the Daedra, you can have him do only certain Daedra quests because "it's what the Aedra would want me to do" (in which case I should think he would just do the things that Meridia/Azura want him to do without DOING the Daedric shrine-quest) etc.