In statements like this:
No creo que él te comprenda/comprendiere.
I don't believe that he'll understand you
Should subjunctive in the present or future be used? Is it "comprenda" or "comprendiere"?
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The future subjunctive is practically obsolete in Spanish. Nobody uses it anymore except in some very formal contexts (legal texts and the like). You can very well do without it while you study Spanish.
In this example of yours, moreover, the future subjunctive sounds very awkward. I cannot explain why, but it looks completely out of place. I have seen it used with:
and so on, but I've never found it in this construction (meaning negative belief in the future, no creo que...).
Since this tense is practically forgotten, you can forget about it. You'll never use it yourself, and you'll only find it in legal texts, if at all.
"No creo que él te comprenda" is definitely the better choice.
Please note that it is ambiguous without more context. It could mean a couple different things:
a) I don't think he's understanding you / he understands you [the implied time frame is now].
b) I don't think he will understand you (for example, if you present your idea that way) [the implied time frame is the future, for example tomorrow, next week, etc.].
If you want to give a clearer timeframe of the future, you can say
No creo que él te vaya a entender
If you want to give a clearer timeframe of the present, you could say
No creo que él te esté entendiendo
As a side note, "entender" is a more common, and more natural, choice than the obvious cognate "comprender."