When it comes to child custody disputes, courts are generally going to be most concerned with what is in the best interests of the children. This usually includes figuring out which parent will provide a better, or more stable, household.
When it comes to celebrity child custody disputes, sometimes how a celebrity publicly portrays themselves can have an impact on a court's best interests inquiry. This is becoming rather clear in the recent Alex Jones child custody matter. While the judge in the matter has cautioned against turning the custody trial into a trial of Jones's talk show persona, there will likely be some evidence introduced linking Jones's real personal beliefs to the conspiracies and hate he promotes on his show.