Because "nut" and "drug" are single, accented syllables, and the preceding words "some kind" are doubly accented, sounding rather heavy and spondaic, the addition of an article in those particular instances lends a more flowing, dactylic feel. I might prefer the articled version with those single-syllable nouns if I'm being informal and trying to get the expression out quickly.
When the object of the prepositional phrase is of two and three syllables, on the other hand, it sounds less fussy without the article. So I think the choice is mostly related to the rhythmic qualities of each phrase.
Semantically, there seems to be a slight change but it's hard to pin down what that might be.
Spoken English often expresses meaning through vocal emphasis on certain words, so changing up the rhythm can subtly affect that output. English teeters between Latinate and Germanic roots, Germanic words tending to be unisyllabic and feeling more punchy and authoritative while Latinate options sound more theoretical and distant. That's why I think we prefer the article-less forms in these examples. But too much punch is jolting. We need flow as well. Adding "a" to the "screwball exercise" pulls it way off in the other direction and so makes it sound more humorous, like your cranky uncle gearing up for a rant.
Perhaps it might be argued that "nut" and "drug" are categories with well-defined members from which to choose, whereas membership in categories such as "relationship" and "screwball exercise" is more loosely defined. Therefore saying "a drug" or "a nut" lends a specificity to the subject being surmised at, that would not fit with the latter qualifiers. But regardless I tend to think that that choice, to add the article, is always optional.
Conspiracy is one of those groups without well-defined varieties, so I think to use it with the article here is to miscategorize it according to this tentative rule I've proposed. If someone did add the article, particularly in informal spoken English, I would think they were trying to be more colorful and dramatic by manipulating the rhythm of the phrase.