Pretend you don't know what the last word of the sentence is for a moment:
Harry couldn't believe that anyone could be so <adjective>.
Harry is (inwardly) expressing exasperation that someone possesses a certain negative trait (expressed by a following adjective phrase) to such a large extent.
In other words, it's clear that so (meaning "to such a large extent") is modifying a following adjective phrase. Even if you don't know what the next word is, you can be pretty sure it'll be an adjective! Take a look at some other ways you could fill in the blank:
Harry couldn't believe that anyone could be so stupid.
Harry couldn't believe that anyone could be so callous.
Harry couldn't believe that anyone could be so self-centered.
Parsing it as a verb form would be infelicitous (and only marginally grammatical at best). This would require so to mean "in that manner" instead, which clashes with the overall tone and meaning of the sentence. So the alternative is very unlikely.
Our only choice is to read interfering as an adjective meaning "meddlesome". This is true even if interfering isn't commonly used as a predicate adjective.