This article
implies that the candidacy of a frum Jew for a judgeship is endorsed by R’ Belsky.
To assume that it is against halacha to hold a judgeship in a secular court would also imply that the judgeships of several ehrliche yidden were obtained without halachic consent, and I don’t believe that to be the case.
There is a well known story that when two litigants representing two sides in the Bobover dispute appeared before a frum judge, the judge recounted a meeting with a gadol after his election (some three decades prior). When he asked the gadol for advice on how to act as a judge in a secular court, the gadol told him that whenever two Yidden appear before him, he should try to get them to go to beis din. That gadol was the Bobover Rebbe, ZT”L.