This is not so complicated. The judge is a member of a La Raza organization, and as such his impartiality is in question when hearing a case from someone who is the nation's strongest advocate against illegal immigration. This is not the same as having the level of evidence for a lawyer to file a formal recusal demand, but it certainly enough that anyone with common sense would question the propriety of his overseeing this case. That La Raza connection cannot be overstated, as it is an attachment to a group that deliberately titles itself after a nomenclature "The Race" that is deeply connotative not only of racism generally, but of a specific agenda regarding amnesty for all illegal immigrants...and worse...the forcible return of the Southwestern portion of the United States to Mexico.
While the judge himself may or may not support all aspects of the La Raza agenda, and while the La Raza Lawyers Association is not the same as the National La Raza Council...though it makes sure to link to the La Raza Council from its own webpage...he is tainted, at a minimum, with the appearance of impropriety. Were he a truly principled judge, he would voluntarily recuse himself...something judges often do when evidence is insufficient to force their legal removal from a case, but in which the appearance of bias is notable.
Here's the problem -- there are a ton of associations for female lawyers/judges, and the same for black lawyers/judges. If you dig into what most of those groups have said at one time or another, there's a very good case to be made that they evince an institutional bias/preference for members of their own groups. It's rather amazing -- some of the women law associations openly encourage their members to hire more female attorneys, promote them, give them better cases, etc.. It's out and out advocacy for gender discrimination, but it's the norm. I actually resigned my partnership in a large firm because some young male associates were getting the absolute shaft because they were not female, and the firm wanted more female partners so they were openly funneling the best work to them.
Anyway, my point is that if this judge were to recuse himself for membership in La Raza, I don't think there's a principled reason to not also seek recusal of judges who are members of the NAACP or various Women in Law organizations. Maybe the correct answer is that they
should all recuse themselves in cases where those beliefs may be at issue, but the fact is that it
never happens, so expecting this judge to recuse himself simply because of membership in La Raza is unrealistic, and perhaps unfair.
I think if you're going to seek/expect recusal, the key is to find specific statements or actions by the judge that show that he personally supports beliefs that are objectionable. After all, a whole bunch of people join professional organizations not because they necessarily ascribe to the views, but simply for basic networking. So if I judge has made specific public statements on an issue, whether in a speech to La Raza or otherwise fine. I just don't think membership alone can, or should, get you there.