While a security certificate is not required, it's definitely recommended.
Security certificates are what web browsers look for to place the green lock icon on the left of a site URL.

Seeing that may help your customers feel more confident about entering their personal data into your site.
While MemberPress doesn't require a security certificate for its basic use,
please note that some of our supported payment gateways, such as Stripe, Square and Authorize.net, do require one.
For the exact SSL/TLS security requirements of those gateways, please contact their support directly.