I'm always amused by the way white people, upon being told that they, by and large, have been brought up with certain privileges that have the potential to blind them to the plights that people of other races go through daily, seem to act so often as if they have been personally affronted and that they are being made to 'feel guilty' about it.
No one is asking you to feel guilty about it, just that you recognise that such privileges exist, and therefore other people's lived experiences may be harder than you. As fun as it is to claim that others just need to 'pull themselves up by their bootstraps' or that you are just as oppressed as they are, you are not.
Speaking as a white, straight guy in Australia, while we don't quite have the same level of race problems in our country, I assure you that they are there. And as a straight white guy, I am accepted as the 'default' human being - I recognise that some of my non-white, and female friends, and particularly my non-straight and non-white female friend, all have lived experiences that see people second guess said experiences, cast doubt upon their daily intentions, and treat their opinions as less legitimate than if I had voiced them, despite said opinions stemming from their actual professions.
You are not being told to feel guilty. Trust me when I say that no one thinks you are so important as to need to feel guilty on behalf of another race. You are not that important.
What you are being asked is to recognise that racism and oppression exist in systematic, engrained cultural ways. They intersect in interesting ways - a homeless white guy might be subject to more suspicion and poor treatment than an upper class black man, but nevertheless distinct patterns emerge that operate upon racial, sexual, and class lines.
To recognise that such unfortunate systemic patterns exists means that you yourself can better yourself as a person by taking such things into consideration instead of thinking of people as existing upon the same flat slate. It means that you won't be part of the categories that second guess people's own lived experiences and gaslight them just because their own life story does not match up with yours. It means that even if you don't do any activism or work against oppression, you at least won't be part of the problem. It means attempting to recognise that you have blind spots, and aiming to correct them.
Not a race but a gendered example that nevertheless works, when I was in college (Aus colleges come before uni), a female friend of mine after a group conversation pulled me aside and told me that she was uncomfortable with how I never took a fact that she said seriously until another guy corroborated it, despite never doing the same in reverse. Not only that but she was the only one studying the actual subject being discussed. Since then I was made aware of how many women even in their professional fields are second guessed, and so from that conversation on I have made a conscious effort to avoid that, to the point where now I don't.
I was not being made to feel guilty, I was simply made aware of a cultural bias that pre-existed me, but that I was nevertheless a participant in perpetuating it. Recognising that not only made me a better person, but has made my conversations more interesting.