Here's an interesting one: how do you think the parties will develop on crime? The GOP has long been known as the tough-on-crime party, a position they emphasized historically when they wanted to appeal to the suburbs and the well-to-do. While movements like Black Lives Matter in the liberal sphere have reinforced this, Democratic growth in the suburbs could potentially shake things up.
What does crime look like in the future? The trendy answer is less violent crime and more cybercrime, but economic downturns and wealth inequality could make people more desperate. Also, how will legislation develop on hate crime? How about drugs?
With BLM-type movements specifically, it depends on what future wedge issue(s) cause black voters trend R; I agree with Skill and Chance that this will happen to some extent. Although for the Republicans to win over 1/3 of the nonwhite vote they will need to make smaller gains among Latino, Asian, and multiracial voters too.
I'd like to think that the Dems will focus more on cybercrime and white-collar crime, while the GOP will be more concerned with property crime and drugs.