There's a huge difference between 'unspecified' and 'nonreligious'.
There might be unspecified options in BG I+II, but it would take an awfuly selective memory to come to the conclusion that Paladins and Clerics in the original Saga were nonreligious.
Paladins in those games are followers of one or more of the deities Torm, Helm, and Tyr.
Clerics either follow Helm, Lathander, or Talos (Tempus and Tyr with the EE). Aerie and Viconia don't have specialty classes but worship their own unique gods. Anomen isn't a specialty cleric either afaik. Not choosing a specialty class does not equal not being religious in BG I+II.
Anyways, in regards to BG III, there has been evidence found and referenced from the PHB, SCAG and the twitter account of the creator of the setting. 5e Paladins *do* get their power from the gods in the 5e Realms. Whether Larian is going off of this popular misconception, or cut it to time/labor restraints, or it's just the way 5e is going and WoTC want's Paladins to be divorced from religion in all settings now, incl FR......either way it is extremely disappointing. It might not mean as much to a casual D&D fan, but for me retconning out an essential aspect of the setting. Larian's played fast and loose with the setting in a few ways in EA, but above all others this one bugs me the most.
In BG2, as a Paladin you can join the Order of the Radiant Heart (it is their "stronghold"). They venerate Torm, Helm and Tyr. It's the order Keldorn is a member off and the one Anomen wants to join too. Keldorn worship Torm and Anomen worship Helm even if he is unkitted (because he's a dual class and the game doesn't allow you to select a kit on class #2).
And I do think WoTC wants to move away from gods being super important in the Forgotten Realm settings. They already setup the "rule" that gods are way more silent since 1489 DR. And way too many people are complaining about it (why don't they play in another setting?). I personally think it's what makes the charm of the FR setting: whatever you do, you're just a cog in the divine order/scheming and if you don't worship someone a little bit you might as well be dust...
Also, Larian had Paladin with deity selection since the first early access version. It was datamined a long time ago. The lines are still in the game files and can be enabled in-game, they hide it for patch 9 so I don't think the idea came from them...
