TL/DR - RAW prior to the publication of The Complete Book of Humanoids would allow for PC Ogre Specialist Priests of Vaprak. The publication of The Complete Book of Humanoids created an alternative ruleset for PC Ogres.
The Monster Mythology book does have instructions on applying class levels to Monster Manual entries - If the class level is less than the monster's Hit Die, just apply the class features to the monster. If the class level is higher, add to HD, saving throws, Thac0, etc to bring up to class level.
Additionally, I noticed the Monster Mythology book was originally published in 1992 while The Complete Book of Humanoids was published in 1993. Presumably, the contents of Monster Mythology was meant for monsters then, not (N)PCs.
The DMG does provide rules for PC monsters though, with Ogre being one of the examples. The DMG rules almost exactly follow the Complete Humanoid rules for Ogre, the major exception being allowed Intelligence. The DMG states that below average Int monsters should be limited to a 16 Int as players, while the Complete Humanoid book caps PC Ogres at 8, the same value attributed in the Monster Manual (note 8-10 Int is the average human range so they aren't even below average).
These DMG rules also set level limits based on the PC's prime ability score for the class. A 9 Wis, which is the Complete Humanoids Ogre's max, allows for a max level 3 Cleric. Given the MM entry on Ogres allows for level 3 Shamans, it feels like the writers of the Complete Humanoids chose that Wis max for that reason. I get the feeling they didn't cross-reference Monster Mythology at all.
I have the 6th print of Complete Humanoids, printed in 1999, so they had 6 years to address this discrepancy and didn't, further making me think it was intentional.