Unearthed Arcana is not tuned for multiclassing.
As per this Jeremy Crawford tweet,
Unearthed Arcana material isn't tuned for multiclassing.
Therefore, there is no developer intent underlying these rules, which makes it difficult or impossible to determine the "right" answer. It's always worth noting that UA material is still in progress, and the designers know that much of it might be overpowered:
Reminder about playtest material like Unearthed Arcana: it's not official, and it's usually more powerful than official material.
Ruling: It's probably OK in this case.
In the absence of any official interpretation, we can try to see what a good ruling would be. I think that it's not unreasonable to allow double-dipping in this case.
There's a lot of precedent for getting extra skill proficiencies and bonuses through multiclassing. For example, you could be a multiclass wizard/rogue instead of wizard/cleric, and get a similar effect from the Expertise feature (as long as your background gives you the necessary proficiencies).
Additionally, the benefits of the knowledge domain are rather weak for a multiclass wizard (a slotless Suggestion and object/area reading). When you compare them to other Arcane Traditions, such as the War Magic one in the same UA, choosing to be an Knowledge domain Theurge seems a bit weak, even if you allow this double-dipping of proficiencies.