Ainur the HOLY ones

[AbercrombieOfRohan]

There is no evidence of any kind of churches or religious areas in the Shire is there? (Besides the taverns)

And what about the Gondorians? Because they are descended from the Numenoreans so it would make sense for them to worship Iluvatar, but they also forgot their history, except for the special few, historians, kings etc.

Or also the Rohirrim, because they are men, they would've worshipped someone right? In theoden's death scene he says,

Grieve not! It is forgiven. Great heart will not be denied. LIVE NOW IN BLESSEDNESS; and when you sit in peace with your pipe, think of me!

And in the same chapter when Eomer finds Eowyn on Pelennor he says

Eowyn, how come you here? What madness or DEVILRY is this?

[Encaitare]

Although I'm not sure about the worship practices of the people of Rohan, they did recognize one of the Valar above the others: Oromë, whom they called Béma. I quote The Encyclopedia of Arda (grand site that it is):

Béma
The name used by the Northmen for the Vala the Elves called Oromë. As the great huntsman and horseman of the Valar, he and his steed Nahar were known to the horse-loving people of Rohan, who claimed that their great horses the mearas had ancestors brought out of the West by Béma himself.