If the Haredim “deserve” some corner at the Wall,
why shouldn’t the Reform?

Judaism is inclusive and forgiving even toward fakers.
Therefore and accordingly, the Haredim too should be allowed something at the Wall.

I didn’t really understand why this is a semantic question.
The key point of the question was the simple understanding that a member of one religion who comes to pray at a holy place of another religion needs to respect the rules of the place.

Do you mean, for example, that Christians could also come pray and make the sign of the cross with crosses and fish and so on?
Or do you agree that it would make no sense to allocate a place for Christian prayer, while still thinking it is appropriate to allocate a place for Reform prayer?

The question of whether the Reform are a stream within the Jewish religion is semantic. As for whether they should be allowed to pray at the Wall, I already answered that. Now you’re asking whether the same applies to Christians. I already answered that above too, and I’ll repeat it again: in principle yes, if this really were a holy place for them and not some new invention. Just as on the Temple Mount, both Muslims and Jews should be allowed to pray there (unless, perhaps, you oppose allowing Jews to pray there. I certainly do not). There are no ownership claims here, because this is not a private place (like a particular synagogue or mosque, where of course only the owners may use it as they see fit), but a public site with value for a broad public, and therefore a democratic state should allow anyone who wishes to use it in a reasonable way.