[RPG] What are the consequences for an illithid rejecting his brain diet

In general in play they were ignored or just treated as an abstract language with no further comment.

As to where they came from, here's an answer from Gary Gygax on Dragonsfoot!

As D&D was being quantified and qualified by the publication of the supplemental rules booklets. I decided that Thieves' cant should not be the only secret language. Thus alignment languages come into play, the rational [sic] being they were akin to Hebrew for Jewish and Latin for Roman Catholic persons.

I have since regretted the addition, as the non-cleric user would have only a limited vocabulary, and little cound [sic] be conveyed or understoon [sic] by the use of an alignment language between non-clerical users.

If the DMs would have restricted the use of alignment languages--done mainly because I insisted on that as I should have--then the concept is vaible [sic]. In my view the secret societies of alignment would be pantheonic, known to the clerics of that belief system and special orders of laity only. The ordinary faithful would know only a few words, more or less for recognition.

In other words, it was supposed to be more like religious languages, but wasn't really well thought through. It disappeared in Second Edition and was not missed.

The item description you bring is unclear. Is "only the most evil of humans could wear such a vile item" a part of the item's mechanical aspects? Or just a description of the item?

If the former, D&D's Use Magical Device skill can bypass it, since it explicitly allows a character to activate an item's power regardless of alignment:

Emulate an Alignment

Some magic items have positive or negative effects based on the user’s alignment. Use Magic Device lets you use these items as if you were of an alignment of your choice.

Other systems that don't have alignments as part of their mechanics will probably not have any such feature.

However, if this is only a part of the item's description, then I would say that any character can wear it - it's not a question of activation - but it's a morally reprehensible thing to do. So your Chaotic Good Bard, if he uses it, is perhaps not as Good as he thinks he is. Is he wearing it because he feels the end justifies the means? Wearing it can further Good, by doing evil? This could lead to a great story around character development and fall from grace. But don't mix game mechanics questions (which should be stated explicitly in the item description) with moral choices.

Without knowing the specific details of the item in question, in the context of the system it's in, it's hard to give an answer.