Inobtrusive versus unobtrusive

I would argue that they are interchangeable and that there is little variation in their meanings. In fact, it seems that inobtrusive is just a variation of unobtrusive, and many dictionaries cite unobtrusive as a definition for inobtrusive. According to Google Ngrams, the variant inobtrusive is almost nonexistent. The spellchecker for this very editor doesn't even recognize inobtrusive as a word. In general, I'd stick with unobtrusive.

They are just synonyms, inobtrusive being the less common variant as shown in Ngram.

Unobtrusive

• Not undesirably noticeable or blatant; inconspicuous.

Inobtrusive:

• Not noticeable; unobtrusive.

(AHD)

Ngram: unobtrusive vs inobtrusive

Un-:

• prefix of negation, Old English un-, from Proto-Germanic "un".

• The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words.

• It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.

(Etymonline)