Gay Friendly Rye although often overused the term is entirely reasonable when used in this context. Rye is probably as Gay friendly as London and Brighton.
Some business will say they are Gay friendly and others are Gay Owned, Rye is a culturally diverse town and everyone is welcome.
Places to Stay and get married in Rye
One very popular venue is Saltcote Place 5 star Gold, secure off road car parking, 01797 222220 http://saltcote.co.uk or to get married http://SaltcoteWeddings.co.uk/
There are other places which are gay owned and certainly gay friendly.
See https://www.visitryebay.com/bandb/aviemore-rye/