Yeah, I was on reddit earlier and someone posted this quote from the phb:

“a paladin’s power comes as much from a commitment to justice itself as it does from a god"

Apparently the SCAG specifically points out the connection between gods and paladins.

Lastly, Ed Greenwood mentioned how atonement works, and also mentioned the phb:

"If a paladin transgresses against their oath, the usual absolution, as the PHB states, is to seek absolution from a cleric of the same faith. "(emphasis mine)

I don't have access to the SCAG or PHB right now, so someone else would have to verify this, but it's pretty clear to me that deities and paladins still have a strong connection in 5e Forgotten Realms, and that the oft-repeated claim that 'in 5e (Forgotten Realms) you don't need a deity anymore to be a paladin is some sort of fanon/misreading that's just been repeated enough times that people just take it as factual without looking into it.