Nitpicking grammarians don’t tend to correct speech; in fact they probably talk just like you do. And if they don’t now, they will when the subjunctive altogether slips away from the language.
But since you asked . . .
Let’s say that it’s is elided in front of best. The expression it’s best, like it’s essential and it’s important, is followed by that (not if), and it triggers the “present” subjunctive (which uses the bare infinitive). Here the grammatical person is changed so you can better see it:
It’s essential [that] I be on time. (Not *It’s essential if I be on time.)
It’s essential [that] I not be late. (Not *It’s essential [that] I do not be late.)
It’s best [that] he know. (Not *It’s best if he know.)
It’s best [that] he not know. (Not *It’s best [that] he do not know.)
So: Best you not know. (Not *Best you don’t know.)
Let’s say that it would be is elided in front of best. Now we have an “unrealized” conditional (followed by if — not that), and it triggers the “past” subjunctive (which uses the past tense except with be in the first and third person singular):
It would be best if you didn’t know. (Not *It would be best if you
don’t know.)
It would be best if he were unaware. (Not *It would
be best if he was unaware.)
So: Best you didn’t know. (Not *Best you don’t know.)
Let’s say that it will be is elided in front of best. Now everything seems to be business as usual:
It will be best if you don’t know.
So: Best you don’t know.