According to this, questions such as these should be no problem:
"Ms. Kagan, are you a Lesbian?"
"Ms. Kagan, please cite the Constitutional authority for special rights to certain groups."
"Ms. Kagan, are you a Socialist?"
"Ms. Kagan, if the government has the ability to force one to purchase healthcare insurance under the 'Commerce Clause", what are the limits of government? In other words, can the government control all of you purchases?"
"Ms. Kagan, what is your Body Mass Index? Do you believe that the Administration's plans to monitor the BMI of every child in the country is Constitutional? Under what article?"
And she will truthfully answer all of these.