Senate Republicans have called on the IRS to investigate various nonprofits that have helped organize university protests, and see if they should be stripped of their tax exemptions. Would that be permissible?
[1.] The government can't strip groups of nonprofit status based on their ideological viewpoints. This was first made clear in Justice Brennan's opinion in Speiser v. Randall (1958), which struck down a denial of a property tax exemption to people and organizations that "advocate[] the overthrow of the Government of the United States … by … violence … or who advocate[] the support of a foreign government against the United States in the event of hostilities":
[A] discriminatory denial of a tax exemption for engaging in speech is a limitation on free speech. It is settled that speech can be effectively limited by the exercise of the taxing power. To deny an exemption to claimants who engage in certain forms of speech is in effect to penalize them for such speech. Its deterrent effect is the same as if the State were to fine them for this speech…. [T]he denial of a tax exemption for engaging in certain speech necessarily will have the effect of coercing the claimants to refrain from the proscribed speech. The denial is "frankly aimed at the suppression of dangerous ideas."