Either form is acceptable.
I think you have to define what you mean by 'acceptable', Set. It's not standard, though I must admit that it is much more common than I had thought.
He asked if it were acceptable.
This is also not standard. Using the subjunctive form as you have done here [and often do] is a hypercorrection
, "A construction or pronunciation produced by mistaken analogy with standard usage out of a desire to be correct," [AHD].
In English, the subjunctive form is used to express irrealis or great doubt. Yours, "He asked if it were
acceptable", does not express either of those. It is an 'if' that is equal to a 'whether'.
He asked whether it was acceptable.