Could the IRS Deny Tax-Exempt Status to Religious Schools That Discriminate on the Basis of Sexual Orientation?

No, not at this time. In my opinion, the courts would allow the Internal Revenue Service to deny tax-exempt status to religious schools that discriminate on the basis of sexual orientation only if Congress made such discrimination in education illegal. If Congress does that, then of course no school that engages in acts of illegal discrimination should be entitled to claim tax-exempt status.

Would an Executive Order Banning Discrimination on Basis of Sexual Orientation Be Constitutional?

Gay rights groups have strongly criticized President Obama for refusing to issue an Executive Order banning employment discrimination on the basis of sexual orientation by federal contractors. In my opinion, the President could issue an order prohibiting government agencies from discriminating on the basis of sexual orientation. However, I believe that the President lacks the authority to prohibit discriminatory action by private businesses that are under contract with the government.