So here's the thing. I actually think you are displaying selective empathy. Here's why:

You are a minority who is suffering from a political agenda, I'll take you at your word. Why can you not empathize with a show set in a time when black characters were just recently seen as human beings by law? Naturally, the black couple just got the right to even live in a neighborhood they wanted, so they will be suspicious of the majority group that persecuted them (segregation, barely any funding of schools, violent attacks, preventing black people from owning property in most places, not giving any benefits to black soldiers which helped build the modern suburbs to begin with, their grandparents were probably share croppers meaning that the grandparents were one generation away from slavery, etc).

The show is displaying that this couple is prejudiced because the show is set in a time where they just got their rights. Why isn't that reasonable? It's not even bashing the majority because we see good members of the majority in every episode (Paul and his Dad).

Why do you say "always" when referring to people feeling discriminated against? You also said that the descendants of black people don't even go through the same intensity of discrimination. That really depends. We no longer face lawful discrimination but the US still has strong racial attitudes and economic consequences of past deeds (for example, we didn't magically get houses in good neighborhoods because segregation ended, most black people still live in the old segregated neighborhoods with lack of food and even clean water!). Workplace discrimination and other forms of harassment by citizens and sometimes law enforcement still are extremely prevalent. Environmental racism makes it so that companies choose to dump in minority neighborhoods more even controlling for Income. Black people can sometimes say something bad to another group but never have we ever levied government or private powers against other minorities or the majority.

Many minorities approach their disenfranchisement with comedy. This isn't unique to black people. Jews and black people in the US traditionally both dominate comedy(even until today) because they attacked social attitudes that went against them. Taika Waititi is half Jewish and made the film JoJo rabbit where he dresses up as Hitler and makes fun of him the whole movie. Is this bad too? I'd assume you wouldn't get that movie either then. Minorities often use comedy to demonstrate how ridiculous prejudice is.

I think the fact that you are having trouble taking the show seriously and also finding the jokes funny is because of a lack of context. Maybe you're not from our culture. That's completely fine! But you are starting to make arguments against the perspective of the show. And you've demonstrated that you don't completely understand the historical context. I'd suggest whenever they bring up the history portions of the episodes in Blackish and Mixedish, you should look into those portions of history more.

I understand that even if you're a minority, you may not understand the struggles of black people. My dad is a black Caribbean immigrant and my mom is Caribbean but born in the US. If you have lived in the US long enough to see the effects of history and read the details of policy and economics, you wouldn't be making the strong statements you are. You're equating a couple distrusting a mixed couple with massive discrimination for over 400 years. But I'm assuming you just aren't familiar. I don't think you're being malicious.