AMERICAN FORK, Utah — Minivans circled the shop like wagons in a western epic. Employees passed giant cups through a drive-through window. And inside, a woman named Taylor Warner reveled in her bit role in the battle that has overtaken Utah: the soda war of 2015.

“It gets wildly heated,” said Ms. Warner, 21, an assistant manager at Sodalicious, a soft drink shop where a team of mixologists tossed shots of coconut syrup into schooners of Dr Pepper and sent them out the door.

So-called dirty soda shops have woven themselves into this state’s fabric in recent years, offering concoctions spiked not with liquor but with flavor shots — a winning business model in a deeply Mormon state where alcohol and coffee are largely off limits and where sugar is the vice of choice. At Sodalicious, best sellers include the Extra Dirty Second Wife (Mountain Dew, fruit syrups, a shot of half-and-half), while down the road at a drive-through called Swig, customers like the Missionary (Sprite, tiger’s blood syrup, coconut cream). Doctors, needless to say, are not thrilled by the trend.