Party registration is public data in Arizona. They provide a ton of data, actually. A lot of states just provide name and party affiliation and maybe zip code or whatever. But you can often just buy it.

If they required people to RSVP, it’d probably be pretty easy for a political party to cross reference and check ID. (It seems Arizona sells the list to political parties and mere citizens have the right to inspect the voter rolls. Whatever that means.)

Source: https://www.ncsl.org/elections-and-campaigns/access-to-and-use-of-voter-registration-lists