This is contentious, and ideological.
I’ll just give my answer, as a middle-aged white cis het male.
I have judgement. I have opinions. I am not disenfranchised from having opinions or judgement, simply by accident of what privilege I have inherited. I am entitled to discuss those opinions, and so long as I do so openly and receptively and respectfully, that is a good thing.
That said: I am privileged, which means that I have a hegemonic* perspective. The kinds of perspectives that I naturally align to get heard a lot, and are familiar to me and to my interlocutors. The kinds of perspectives that my less privileged interlocutors may have are not necessarily as familiar to me.
Which means that while my judgement and opinion is as valid as any other’s, I readily concede that I have more to learn from the less-privileged than they from me, about the realities they confront. And being open to learning means that, a lot of the time, I withhold judgement, and I don’t interrupt, and I just listen. And because my privilege is the kind of privilege that drowns out others’ voices, I don’t pipe up with my opinion and judgement until it’s appropriate to: it’s not all about me.
Is the reflex cry of mansplaining and whitesplaining good citizenship and good alliance-building? No, because reflex cries are not discourse, they are turf-guarding. But if the less-privileged have carved out a space to speak to their lack of privilege, then the more-privileged are in that space as guests; and it is courteous to act like it. Offer your opinion, but offer it courteously, and with a bit of deference.
If they keep shouting you down, and you are honestly speaking in good faith with them—why then, there’s no discussion to be had; shake the dust off your shoes, and move on. But do make sure you’ve been listening, and trying to learn.
*If Sam Morningstar’s Tourette’s syndrome involves saying “neo-Marxism”, mine is saying “hegemony”.