I think education is actually a priority to poor families. Their needs are different, presenting different challenges. One example...transportation needs are different. Poor families struggle getting their kiddos to/from school and/or other educational opportunities. If the parents are working or don't have access to another vehicle, many opportunities are limited. Address the transportation challenges and those kiddos (and their parents) would love to participate.
And why the fight? Those in the public school system are selfishly protecting their interests, not what's best for the kiddos. They are protecting their salaries, their lavish facilities and infrastructures, etc.