If students are protesting your participation in an event
Inviting speakers, including provocative or controversial ones, is an essential component of free speech that can inject fresh ideas into a campus. Talks that provide a diverse array of opinions can foster campus-wide contemplation and discussion. The same holds true for events involving faculty.
Be prepared to defend your ideas against vigorous criticism. If you find that you cannot defend them in the face of such criticism, take the opportunity to critically reevaluate your position.
Having a right to say something does not imply that you should say it. As a faculty member, you have a responsibility to help further reasoned debate and dialogue. Consider carefully what your intention is in speaking at the event in question. Are you trying to further productive discussions, or are you merely trying to be provocative?
Just as you have the right to speak in a forum to which you were invited, others have the right to vigorously protest your appearance. Unless the protests are disruptive enough that you are unable to speak or be heard, they should be treated as a permissible exercise of free expression.
Make sure that you are receiving equal treatment and that even if your administration’s values differ from your own, administrators treat you with a content-neutral approach.
There are many organizations (like FIRE) that offer advice, legal support, and public advocacy if a college or university limits a faculty member’s speech rights. If you feel overwhelmed, reach out.