I do not find this to be a convincing argument.
Your confidence shows you might have a deeper insight into the rules than I do.
The fact that something can be a class feature and grant a proficiency is not an actual rules problem from the Multiclassing perspective as both can be true at the same time. The Nature Domain is a Cleric class feature, which is allowed by the multiclassing rules, but also grants a skill proficiency, which is disallowed under the multiclassing rules. There is no inherent contradiction. (I suppose you could argue that the rules mean the proficiency is both allowed and disallowed at the same time, but then arguing for some sort of Schrodinger's proficiency doesn't exactly help your case.)
Sorry, I didn't read under the 'class features' header that it says that you get the class features as normal, unless they're proficiencies. You're adding information not present. The rules say, "[w]hen you gain a new level in a class, you get its features for that level." There's nothing in the handful of exceptions that changes that with regard to proficiencies provided by those features.
I think the best counter-argument here is to point out how it impacts the first level Knowledge Domain feature. That feature grants proficiency in two skills, and then gives expertise to those skills. The way it is worded, denying proficiency would subsequently deny the expertise. One can fairly argue that denying first level proficiencies granted by class features makes sense, but it is harder to argue that Knowledge Clerics should be denied their expertise.
I think the best counter argument is that you get the class features, period. If those include proficiencies, as many do, you get them.
Here, let me try this way. When you take the cleric class, you get a set of proficiencies: armor, weapons, tools, saving throws, skills. These aren't tied to level -- they don't appear on the level chart as features you gain at that level. These are the things you get at the very beginning when you choose the class. Then you look at the features by level chart for the class, find those in the class descriptions, and apply them as necessary. These are the things you get from that class for your level in that class.
Multiclassing changes the first thing -- the things you get for just picking the class -- but not the second thing -- the features you get at each class level.
Example: As a new, 1st level character, I select cleric. For selecting cleric, I get the following proficiencies: light and medium armor and shields; simple weapons; wisdom and charisma saves; and two skills from the list in the PHB. Then I get the 1st level cleric features of spellcasting and divine domain. My selection of divine domain may give me more proficiencies.
As a different character, I choose to multiclass into cleric at a level above 1st (let's say 2nd). When I gain my 2nd level, I choose the cleric class. The mulitclassing rules, though, change the way I get the starting proficiencies -- the ones I get for picking the cleric class. In this case, for picking the cleric class, I get light and medium armor and shield proficiencies ONLY. I don't get simple weapons, wisdom and charisma saves, or two new skill selections, because those selections have been modified by the multiclassing rules. After I've recorded my (maybe new) armor proficiencies, I get my 1st level cleric features. The multiclassing rules state clearly that when gaining a new level in the class, I get all of the class features of that level. Well, the class features of a 1st level cleric are spellcasting and divine domain. If the divine domain grants me additional proficiencies, I get them because
those are part of the class features awarded as part of gaining a new level in the class.