What would the Romani be doing in Utah? Their traditional lifestyle requires some interaction with settled peoples, since they make their money providing services to them. I don't think the Utes are going to care much for what the Romani have to offer. Maybe these alt-Romani could take up a boertrekker lifestyle as nomadic pastoralists?
We have to understand how the Mormons arrived in Utah, which at the time was just outside or at the border of American jurisdictions The Mormons fleeing persecution and looking for secluded place to live migrated to Utah. They for most part were farmers and some merchants.
now for your premise to happen you need a POD to make the Romani decide to flee early to mid 1900 rural US and seek a isolated place. Then you need to change how Romani economically would worked since majority not farmers.