The spell mind blank says:
one willing creature you touch is immune to psychic damage, any effect that would sense its emotions or read its thoughts, divination spells, and the charmed condition. The spell even foils wish spells and spells or effects of similar power used to affect the target's mind or to gain information about the target.
The Gem Dragonborn Psionic Mind feature says:
You can send telepathic messages to any creature you can see within 30 feet of you.
Could mind-blanked Gem Dragonborn converse mentally with each other?
Best Answer
I would say that Mind Blank has no effect on this.
None of these things say that they prevent telepathic communication. The closest match is 'affect the target's mind,' but 1-way telepathy has no more affect on your mind than someone just talking to you.
However, for a more persuasive comparison, see the Ring of Mind Shielding which says:
By this, we have an example of a magic item that shares some traits with Mind Blank, but specifically calls out that it blocks telepathy. So given that we have a magic item that specifically says it jams telepathy--but Mind Blank does not say that it jams telepathy, it seems a safe assumption that it does not.