Where do you believe is the greatest ideological divergence in the U.S. , between East and West or North and South?

The country isn't divided in such easy to define way. For the sake of discussion the West and East coasts are predominantly Progressive while the middle of the country is Conservative.

I'd say the ideological divergence in the US lays right between loyalty to president and loyalty to country.

Between the coast and the heartland, I would say.

Yes. lol

Isn't it more a question of rural vs urban in a more broad view ?

Coastal versus inland maybe?

More so North and South.

North and south

Neither. Urban and rural are were the biggest cultural and ideological divide is.