No, Alexis is weighted towards AV, but Flauros is weighted towards OO and CoE. In the scenarios he shows a clear preference towards Esus, and explicitly states that he is no friend of any demon although he may use methods just as dark as theirs.
Basium broke the Compact, which while technically more part of the Force than Law sphere is still seen as a major offense by Junil and Sabathiel. He also abandoned his duty to serve his god, and harbors a deep hatred for the new god of this sphere. Basium is not so chaotic that he breaks the law for the sake of breaking the law, but he does not respect any authority save The One. (Of course, he has never met The One and probably misinterprets his will. The One never ordered the forces of good to fight evil, only to protect Mankind and guide it to enlightenment. Force may be needed to protect from direct assault from evil gods, but in general I think The One would side with Sirona and Jesus and say "do not resist the evil one.")
Kael has explicitly stated that Basium has no affinity towards any religion and is personally not religious, but is willing to use any faith (except those who worship demons...and he probably wouldn't like the worship of the god who stole the precept of life from him either) as a tool in his arsenal. (He is actually shown as praying to The One, so I'd say he has a deep faith in his personal conception of who The One is. Like Cassiel and all the gods he seems to think that One One does not want to be revealed, but unlike Cassiel he still thinks there is merit in worshiping him and nothing wrong with encouraging the worship of lesser gods as a tool in fighting the crusade he thinks The One wants.)
The only religion the Mercurians have in the scenarios is the Empyrean. Of course, Basium clearly expresses that he has never thought much of Lugus and is pleasantly shocked to find that his high priest has the nerve to strike against the throne of hell.
Runes fits Basium ok, not great, but probably better than the other religions. Kilmorph is generally too passive for him, but not when she gets really pissed off. The protective mother goddess did stop the last archangel to wage the godswar once a truce was called, but she also agreed to give the Luchuirp an ultimate weapon (The Mithril Golem) when they wanted revenge on a legion of the drowned (which are of course minor demons of the Overlords inhabiting the deceased bodies).
RoK however does not fit the Calabim well. Vampires may hone their skills over centuries, but they enjoy living luxuriously without ever doing an honest day's work, and seizing their chattel's rightful earnings. It is of course not as bad a fit as the Empyrean. As much as they like order (when they are on top) the Calabim hate justice, so following the Order in earnest does not fit. I can certainly see them liking the corrupt Order that persecuted Valin though. (I kind of suspect that the impious high priests of that era might have actually been members of the Council of Esus.)
I'm actually not sure Basium minds the Council of Esus so much. Sure, Esus is evil, but he doesn't really use demons much, even in his hell. He has also been known to betray the other evil gods on occasion, like when he sent the Svartalfar to save the word from Tebryn.
I kind of like pairing the Mercurians with the Illians too. Basium's desire to keep fighting the godswar is rather similar to the nostalgia of the Ice sphere. His hatred for Sucellus could drive him to admire the one who killed him. I often like to role play that Auric seduced Basium to the dark side by promising him that they would slay Sucellus together and Auric would give him the godhood he always deserved.
