[Mumriken]

That is indeed (albeit rather facetiously phrased) what I would consider still being loyal, no matter how "stupid" it sounds

Lol, only an idiot would do that. If that is the only way sauron could be loyal then men and elves would conquer middle earth the orcs would be slain and long gone. No I'll rephrase that...you're the stupid one for saying that is the only way Sauron could be loyal to Morgoth.

Assuming Sauron did establish this religion out of loyalty to Morgoth, this is exactly the "stupid" kind of loyalty you are talking about.

No because later on it led to the destruction of Numenor.

The question is: was he encouraging the Númenoreans to worship Morgoth because he actually believed it would do any good or because it was what Morgoth would have wanted, or did he do it for the sake of his own power?

There is no question to ask...you don't get it buddy.

No, it doesn't necessarily mean he turned against Morgoth, but it doesn't necessarily mean he was still serving him either.

How could he serve Morgoth if morgoth was not in the world???????????????

I guess we could simplify this discussion by analysing this question: did Sauron establish the Melkor-religion among the Númenoreans because he genuinely believed that Morgoth was God and could give blessings to the Númenoreans, in real tribute to Morgoth (or his memory) and because it was what Morgoth would have wanted? Or, on the other hand, did he do it simply out of convenience because it was the most convincing lie for Morgoth's former lieutenant to tell?

He convinced them to worship Morgoth so that they would turn against the Valar...he did this in service of Morgoth AND himself. You say the only way he could be loyal is to put on a chastity belt and attract people to some stone temple where they would sit and pray to Morgoth all day and night...you don't think it's stupid but it indeed is...

I hope I don't have to paste this again...

Sauron is more loyal to Morgoth than he is to the valar by being loyal to himself.