Should we use use the present continuous form "would you mind if" to ask a polite question?
No, you should not. It is ungrammatical to say:
The sequence of tenses needs to be more like either this:
Although some might take exception with one or the other of that pair, both are heard in the wild.
Your sentence as such is grammatically incorrect. You could have used
if you are inclined to using a present continuous form.
Though you are correct in using "would you mind" here, I'd suggest you use, "Do you mind" for questions with similar structure.