Federal law doesn't prohibit it and neither does Utah law. It makes no difference whether the states border or not, it just has to be legal in both the state in which the long gun is purchased and the buyer's state of residence.
Interstate private party sales are prohibited.
Q: From whom may an unlicensed person acquire a firearm under the GCA?
A person may only acquire a firearm within the person’s own State, except that he or she may purchase or otherwise acquire a rifle or shotgun, in person, at a licensee’s premises in any State, provided the sale complies with State laws applicable in the State of sale and the State where the purchaser resides. A person may borrow or rent a firearm in any State for temporary use for lawful sporting purposes.
[18 U.S.C. 922(a)(3) and (5), 922(b)(3), 27 CFR 478.29 and 478.30]