Purists argue about everything, including the inclusion of the salt rime.
For me I like one of two versions: Juice a lime, add a shot of reposado, either add a 1/3 shot of triple sec/cointreau/grand marnier OR twist a section of sweet orange into the drink. Shake over ice. Salt rime optional. (Sairey Gamp loves it, I’m indifferent.
Version 2 is more interesting: Juice a lime, twist in the juice from a section of grapefruit, add a shot of reposado. Shake over ice. No salt rime.
For some reason grapefruit and tequila are like Astaire and Rogers. Nothing works together that well, unless God intended.
I use kosher salt which is less attractive, but cuts the iodine flavour. Table salt works just fine, and I’d never send it back if you offered one to me.