Would you mind? and Do you mind?
We use the phrases would you mind + -ing form, and do you mind + -ing form to
ask people politely to do things. Would you mind is more polite and more
common:
Would you mind opening the window, please?
Do you mind turning down the volume a little, please?
Do you mind me turning on the light? (I want to turn on the light)
When we ask for permission politely, we can use would you mind if I + past or
do you mind if I + present:
Would you mind if I turned on this light?
Do you mind if I sit here?
When someone asks for permission, we usually reply no …, meaning ‘I don’t
mind’ or ‘I’m happy with that’. If we want to say that we are not happy,
we usually begin with I’m afraid …:
A: Would you mind if we sat here?
B: No, not at all. (you can sit here – I don't mind)
A: Do you mind if I use your phone?
B: I'm afraid the battery is dead.
https://dictionary.cambridge.org/grammar/british-grammar/mind
Do your parents mind you leaving home?
(formal) Do your parents mind your leaving home?
https://www.oxfordlearnersdictionaries.com/us/definition/english/mind_2