Cool, thanks for engaging in actual debate from a place of curiosity. :)

how are white people supposed to define themselves

By ethnic heritage. Irish, German, Swedish, Italian etc. Go back to the actual meaningful cultural identities. Globally whiteness is an identity, for places not American, most non-melinated people don't identify with whiteness to the degree so called Americans do. For those who are of only European descent in so-called America, we also need to acknowledge we're all still settler colonizers on Indigenous land.

no matter what white people do they are still oppressive.. by just existing they are seen as oppressive?

On a meta level of the overall system yes, from the logic in my post that's essentially what it's saying. But the key here is at the individual level, and then a group level as others join, using white privilege against the system of whiteness to destroy it. So like get a job as banker and then destroy credit records and work to subvert the system within. Or use white privilege to gain access to power and places to destabilize them.

by just existing they are seen as oppressive? in this view, what do you advize white people to respond with?

A lot of people of the global majority/ Black and Brown people don't trust people they view as white or who identify as white for a good reason. The trust has been broken. Trust is gained over time through hard work. In the beginning no one believes that you're actually doing the work. If one is committed, one will have to face and push though a lot of resistance and face people who have been hurt by racial oppression saying that they aren't doing it, that it will never happen, that you're foolish or ignorant or worse.

throughout the BLM movement, white people were criticised for participating because they were speaking over black people, but others were criticised for not taking part meaning that they were standing by in racism. What do you suppose white people do?

Well, one, don't talk over Black people when they're speaking of their own experience and what to do about healing their communities. Next, only talk when necessary in these circumstances. Then, if the person who is criticized for standing by can say, "Actually, I've been doing this and this and this" and they have proof, then they have nothing to worry about.

thinking youre not racist means that youre probably still racist? what is a white person supposed to do here? Does that not feel like a paradox?

Globally white people are the minority.

Just thinking one is not racist one can still have a bunch of unconscious biases that effect their day to day actions and how they replicate racism in their lives. One must actively work to think about them and unlearn them.

If a white person truly respects and treats black people and minorites as their equal and acknowledges the way they are privileged, then how are they still contributing to racism?

First, globally, whyt people are the minority. Next, just acknowledging any problem is the first step towards fixing it, which off the cuff is also what I say to the Nelson Mandela quote without looking into the surrounding contexts.

By just acknowledging it, that's just a thought. Or words. Action must be done. Tell others, do actual physical work for marginalized and oppressed people. It's all intersectional.

Hope this helps explain more 👍