It's not meaningful to talk about personal responsibility or guilt when it comes to dealing with issues of systemic racism.

Sure it is. You're asking a vast group of individuals to feel guilty about bad things some of their ancestors did a long time ago. That still doesn't make any sense whatsoever, because these individuals had nothing to do with it.

The idea is that we ought to sympathize with the struggle of oppressed groups and turn that into a push to reform the system; not out of white guilt, but out of moral conviction.

We do sympathize the shit out of them. That's exactly why White Guilt is even a thing. Without the hypersensitive sympathizing, people would see the inanity of feeling guilty for something someone else did.

Yes. Interpersonal racism is treated as an unforgivable sin and a taboo, while systemic racism lies basically untouched.

You can't detach "the system" from the individuals. There is no systemic racism without individual racism, and since individual racism is not tolerated at all, there is no systemic racism either.

Besides, you've got it backwards:

.. We all know that if a white actor joked about how he got to kill black people in a movie, his career would be over instantly.

White people will lose their jobs over racist tweets for example, but a black person can laugh about killing white people on national TV and people just mindlessly "Woooo" at him.

You have no case. Stop spreading misguided ideas.