No, I think when put to the test most liberal people would not do this. If they "tried", why did those neighborhoods wind up 100% black?
Where I grew up, for instance, the second best school in the city (by test scores, at least) was 99% black (mostly the children of alums of a nearby HBCU). White parents would send their kids to worse performing schools with more white kids over sending their kids to that school.
What that also mean is that if one black family moves into white street, every white on that street is at risk to loose exact same things. They become redlined too.
Redlining means that white people have financial incentive to segregate themselves and to push away incoming blacks. Liberal might not mind living with blacks, but will mind being unable to take mortgage he would be able to get otherwise.