There is a very slim chance that there will be a kid rush. As contestants progress they are provided with more assistance which in the case of singers would be accompaniment. Which includes non tznius women singers. If there will such accompaniment, that would be public chilul Hashem. A Kidush Hashem would be if he publicly refused to sing with or shake a women’s hand a say it’s because it’s ossur. In which case I am sure that those who think his appearance alone is a Kidush Hashem will be horrified and claim that the public refusal is chilul Hashem.
Right now this is leaning towards chilul Hashem, like the chilul Hashem of when Mendy and Heidi appearing on tv. ( the other much bigger chilul Hashem in that case was the reaction by some who call them Jewish publicly and loudly violating the Halacha of ” heve Dan Es kol bosom lkaf zechus” and being ever more insistent when it was shown that Heidi was telling the truth. That was the much, much greater chilul Hashem.) I hope nothing of the sort arises such as if he hugs a woman publicly other than his mother and you will have people saying that it’s appropriate.