It is not implied.

For instance, I did not suggest my family is full of bigots. But I didn't write an article titled "All Families Are Bigots."

That families are torn apart by fraught political discussions is a reality for many people, though.

And this word is full of people driven by their prejudices and fears, and they have families, too.

What you did was project your own thoughts and feelings on what I wrote, which is fine. Thanks for reading.