While by default RSVPify will ask for your guest's e-mail address so that they can be sent a confirmation email after they RSVP, you can disable the request for e-mail address entirely.
We take your privacy and that of your guests very seriously, and we will never directly email your guests -- with the exception of sending them a confirmation of their RSVP if you have this setting enabled. All of your guest's information is strictly private, and is accessible only to you and senior support staff (in the event you need our assistance with anything).
To disable the e-mail address field in your RSVP form:
In RSVPify 2.0, go to Setup > General Options.