> Do you live in Utah?
Yes.
> You meet a lot of Mormons and you can often tell who they are, but they are very nice and it doesn't seem to affect day-to-day life much at all.
Well, I didn't say it affected my day-to-day life, I said that it affects local legislation.
> Liquor stores aren't open on Sunday and you can't buy full strength beer in the grocery store. Other than that the differences living here vs. elsewhere aren't huge.
You can't buy liquor (apart from the low-strength beer) from any stores except the state-owned ones. The state strictly limits the number of liquor licenses they give out to restaurants and bars, and the rules surrounding the use of those licenses are strange and ever-changing, such as the "Zion curtain" that forbade bartenders from making drinks in view of the public. The strongest drinks bars/restaurants are allowed to serve are weak, 1 ounce of liquor per drink if I recall correctly (it may be 1.5). For a while they had that weird "sidecar" exception that allowed the establishment to sell you an extra ounce of liquor on the side the customer can mix in themselves. Servers are not allowed to serve you an alcoholic drink if you have one unfinished. Restaurants cannot sell you liquor unless you also order food. And so on.
There was a law (it still may be in place) that forbade car dealerships from being open both Saturday and Sunday. Since no dealer is dumb enough to close on Saturday, this was an obvious effort to force those businesses to close on Sundays.
The state has been very amenable to big land deals with the LDS church downtown, deals they would not have made with any other entity. For example, the City Creek project.
The church strongly influences legislation on things like medical marijuana and gay marriage. For certain people, those influences would very much affect day-to-day life.
This is what I can remember off the top of my head, I'm sure there are more. Like I said, it's mostly a good place to live. But the church currently has too much influence in government.