[Zigûr]

Originally Posted by Mumriken

If it was out of fear, then I would probably agree with you that he never was truly loyal. But if he joined Morgoth for some other reason then I'd say he was loyal.

As I think has been made clear from quotations, Sauron did join Morgoth initially in admiration for Morgoth's ambitions and methods, but as Morgoth's motivations waned towards all-consuming destructive hatred perhaps Sauron's loyalty did as well. Surely otherwise he would have occupied himself with destroying the world in Morgoth's name rather than trying to take it over for himself. Consider when a prophet dies but his follower tries to carry on his work in the name of that prophet. I would consider that loyalty. But if the prophet dies and the follower abandons that work and starts a new one, that would be different. It's the same with Morgoth getting banished to the void: Sauron could carry on Morgoth's work in Morgoth's name, even though Morgoth is gone, but instead he sets about making himself a Dark Lord and ruling things his own way. What's more, he even shows disdain for Morgoth - as some of our quotes from Professor Tolkien established, it seems that Sauron considered Morgoth to be a failure and set up Morgoth as a false god in Númenor despite knowing full well that Morgoth was powerless and that Eru was the one true God.
But to change things up I thought I'd examine it from the other point of view anyway: in what ways was Sauron still following Morgoth? So I'll offer some different material from the Professor. Take this comment of Sauron's doings, for example, from "Of the Rings of Power and the Third Age":

Therefore when Eönwë departed he hid himself in Middle-earth; and he fell back into evil, for the bonds that Morgoth had laid upon him were very strong.

So we can see that Morgoth's evil was certainly responsible for Sauron's relapse - that and his own nature, of course. Morgoth's Ring offers this consideration regarding Sauron's establishment of the Melkor-religion in Númenor:

there was seen the effect of Melkor upon Sauron: he spoke of Melkor in Melkor’s own terms: as a god, or even as God. This may have been the residue of a state which was in a sense a shadow of good: the ability once in Sauron at least to admire or admit the superiority of a being other than himself.

Of course the Professor does qualify this:

But it may be doubted whether even such a shadow of good was still sincerely operative in Sauron by that time.

Professor Tolkien seems to think that really it was a matter of convenience, not loyalty, but it's still worth musing upon. I suppose Sauron could have invented any phantom for the Númenoreans to worship, but can we imagine, perhaps, that as presumably well-educated people steeped in the lore of the First Age that the Númenoreans were well aware of Sauron's prior affiliation with Morgoth and that made propounding Morgoth, rather than some made-up figure, a more believable lie?