It absolutely should make sense lorewise.
The lore is far from dead, full stop. The fact this thread is several pages long speaks to the fact people care about the lore but don't want to admit it LOL.
Everyone getting Priest, Rogue and Mage is easy to explain. Hell, they hand-waved Dwarf and Orc Mages by simply saying someone decided to take the time to sit down and study the Arcane. Human and Forsaken Undead in Cata required no explaination. Neither did every race getting the Warrior class.
NELF Mages in Cata required lore justification for obvious reasons. So did Tauren Priests and Paladins. As others said, Lorewise Tauren Priests and Paladins use Sun Magic but in-game they are Paladins.
The Tauren/HM Tauren and Draenei/LF Draenei are both known for their morality but we've seen shifts in that regard over time. Especially with the Draenei. Velen became friends with Illidan during Legion after all. So, Tauren and Draenei Rogues isn't a stretch.
Draenei/LF Draenei WARLOCKS, on the other hand would be interesting to explain. I mean Draenei have a severe allergy to Fel Magic that deforms their bodies and minds while LF Draenei would probably purify Fel Magic without trying. The only way I can see this working without heavy Retconning is saying during the Argus Campaign, some Eredar Warlocks secretly defected from the Legion and surrendered to the Legionfall. After Sargeras was dealt with, these defectors were secretly moved to Outland just before the Fourth War broke out and forgotten about for a while.
Tauren/HM Tauren Warlocks can be explained as having voluntarily foresaken their cultural beliefs in the pursuit of knowlede knowing their would be considered pariahs by their kinfolk.
Night Elf Warlocks can be explained the same as NELF Mages: A breakaway faction that lived in hiding.
Human Shaman...hmm, only if Orcs get Pallys. Then we'll talk =D