It’s about 50-50.

1964 is of course is a presidential year, so there’s lots of good stats available. 1964 is the last year a Democratic presidential candidate took Utah. Johnson won Utah with 54.9% of the vote. Salt Lake County was even more Democratic than the state as a whole, with Johnson taking 57.1% of the votes. But certain counties like Carbon county leaned even further toward the Democrats giving Johnson 72.7% of the vote.

1964 was a Democrat surge year in Utah. Prior to the vote all offices had a slight Republican lean. The governor was Republican George Clyde. The Republicans held the Utah Senate 13-12, and the House 34-30. The US Senate offices were split evenly between the parties, and both Representatives were Republican. But during the election the Democrats gained the governorship, the Senate, the House, and one of the US Representative seats. While Senator Frank Moss easily defended his seat against the popular and very conservative BYU President Ernest Wilkinson.

In the period it was very possible to be a Mormon and be liberal. The First Presidency of the LDS church in 1964 included Hugh B Brown who had run for several offices as a Democrat and N Eldon Tanner who had spent 17 years in office in Alberta as a Social Credit (Center-Right) assembly member and government minister. While the Apostles included arch-conservative and John Birch supporter Ezra Taft Benson. I can’t think of any communists or socialists, but the LDS church allowed for a wide variety of belief from moderately liberal to very conservative.

Your proposed toy store owner in a place like Midvale, could plausibly be Democrat, Republican, or unaffiliated. He could self identify as liberal or conservative.