You can play the dogmatic cleric that doesn't even have deep understanding of their own god.
Ofcourse you can ...
Im not really sure, but like for 99% you can even play a Cleric that follow certain deity (i believe its Loviatar in this game) but dont recognize fellow worshipper.
By simply not picking [Cleric] choice.

There allways are alternatives.

Paladins are martial warriors with oaths to a god (or cause, but let's set that aside).
I have better idea ... lets not!
Can you provide us some source?
There was lot of quoted about Paladins in 5e dont swear their oaths to Gods themselves, but nothing even suggesting otherwise.
They wouldn't even get [Cleric] tags because being a pro warrior requires total time commitment and their oath more aligns with a valued aspect of a deity (justice, honor, valor etc) than the deity itself.
Now i feel confused.

This sounds to me like you were advocating against Paladins having deity tags. O_o