I’m with the Capn.
While I will concede that not tucking your shirt in isn’t going to have any impact on your ability as a referee, it looks taggy, and, in my opinion gives the impression that you’re not particularly bothered.
Now 12 years in the Grenadier Guards has left me with a penchant for polished shoes and ironed shirts etc.
But it’s about taking pride in your appearance, and rightly or wrongly if you turn up for a match with dirty boots, an untucked shirt etc you will come across as unprofessional, and if you don’t care enough just to tuck your shirt in then what else don’t you care about.