What is the most culturally unique of the lower 48 states?

[If my soul was made of stone]

How unique can Utah be with Idaho having a large Mormon minority and its own branch of BYU?

Utah doesn't have the same backwoods skinhead country as Idaho, or any of the other cultural regions that the other states with significant Mormon populations do that make them more aligned with their neighbors.

[If my soul was made of stone]

In some isolated communities along the state’s coastal area it’s still certainly possible to find people who speak in an English accent in the old Elizabethan form. Or the descendants of former slaves who still somehow have retained a West African influenced form of English.

Neither of these are accurate--the "Hoi Toider" accent is distinct but not Elizabethan, while Gullah is not traditionally spoken in North Carolina except very marginally in the far Southeast---it's much more of a Lowcountry SC thing.

The Hoi Toider accent also exists in pockets of Virginia and Maryland, famously Tangier Island in the former and Smith Island in the latter.