Here is the actual verse from Acts 10:34…
“Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons:
But in every nation he that feareth him, and worketh righteousness, is accepted with him.”
The woman, be refusing to give up her seat, was trying to say that God does not respect or favor one man more than another for something trivial (like matters of race or gender), but for their good works and belief in Him.
Very similar to Dr. King’s sentiments about judging people “not by the color of their skin, but by the content of their character”.