As a whole, resegregation is most certainly something which our society must do all it can to avoid. With a rapidly increasing wealth gap across the board ethnically, such efforts are a core aspect of ensuring that the future American education system truly enables social mobility and the growth and sustenance of the middle class.
Of course, the first step towards this end would be basic efforts of addressing the issue “solved” by Brown v. Board of Education: state-enforced segregation. While many would argue that much of the resegregation that is now occurring is being triggered by natural factors, as opposed to the sort of explicit legislation that established all-white schools pre-Brown, the sort of gerrymandering that prevents white neighborhoods close to majority-black schools from attending said schools could certainly count as such. Explicit prevention of this would be an ideal first step, though it might not foster the sort of city-wide integration that the next step should entail (as it did in 60s-80s desegregation efforts).
Beyond legislation in the same thread as that which initially addressed this issue, the modern educational environment begs a variety of other solutions that can serve as factors in preventing re-segregation (or at least its negative effects). The primary of these would be the provision of financial incentives and funding for specific resources in low-income (and thus often containing large minority populations) areas. The first of these would be providing high-quality training to teachers in these areas, and incentives for high-quality teachers (not Teach for America; this has plenty of problems, too), such as competitive salaries.
One seemingly effective approach to a funding structure that could accommodate these greater demands would depend on flexibility. Since wealthy areas often have the capability to boost funding for such resources through levies that aren’t nearly as effective in low-income areas, this could be a more significant consideration in state fund allocation, which could be skewed in favor of such low-income areas.
With any such equalization of funding, additional programs could also be emphasized in these areas. The two categories into which these would fall are college and career counseling programs, and exposure concerning these. The job of former is made additionally difficult by the fact that, as discussed in the case of D’Leisha in the above ProPublica article, even the most successful of students at these schools face marginal prospects for higher education. As such, counseling resources create a feedback loop with the overall quality of education: of course, it is necessary for such programs to excite students about the prospect of college and educate them about truly accessible opportunities, but in turn this has the potential to positively impact other classroom experiences and contribute to an improvement in their inherent perception of further education.
My reference to an increased focus on exposure to college and career opportunities is based off of research that has demonstrated the lack of minority representation in STEM fields. As such, after-school programs that aim to provide students with basic skills in these areas and, as above, excite them towards the prospects of being involved with them at a higher level, can begin to address a significant aspect of the negative effects of resegregation. Finally, the implementation of all of these has the potential to begin destroying public incentive to stand by segregation (in the form of this inherently creating better schools where low-income students are less common). If ideal resources are universally available, convenience, beyond ethnic or socio-economic isolation, becomes the most important factor in school-choice. The problem fades into obscurity.