Four lesser options, one major one.
Fast-forward the split party part. Don't dwell on stuff as much as you otherwise would.
Snack and bathroom break time. Shoo the other players off. This will serve as a cue to the sneakers that they should include everyone eventually.
Metagame, encourage the group to find ways to include people even when it's suboptimal.
Spring stuff on the other party to keep them occupied. Sure, if they just get a lead, they can wait to follow up, so make the action come to the PCs - someone kicks down the door or otherwise looks to interact with them NOW.
Give them all equal spotlight time. 5 minutes dealing with sneakers or interrogators, 5 with the others. They'll either start going to do stuff of their own accord, or they will, heaven forfend, roleplay with each other.
Number 5 is really my favorite. We've had plenty of great moments while half the party is doing something "important" and the other half goes to a bar and gets in trouble. All you have to do is give them the spotlight time, PCs are notoriously twitchy and impatient and will find ways to entertain themselves, "on task" or not.
My added thoughts based on your question edit.
You don't need to balance "in game" time. If one group went and did something for six hours, but real time that took five minutes, then you just need five minutes of spotlight time for the other group, even if that's five minutes of rousting a hobo and then 5:55 of "we go somewhere and hang out."
If they need ideas for what to do or you want to spring things on them - that's why God created random encounters, right? Either they self-motivate some mission oriented stuff, which you come up with, or they mess around in a tavern or go shopping, which you come up with, or they sit around looking glum till a land shark attacks them, which you come up with. You do anything you'd normally do to the full party, but ideally with slightly less kill. (Or not, if you want to dissuade them from splitting in the future.)
If they are content to wait in the bar, let them wait in the bar. Have fun bar things happen. People hang out in bars in real life, it's fun. And sometimes good and/or bad things happen, hence the larger than usual incidence of hookups and cop interventions in bars. All you need is for them to all be having fun and getting roughly equal "spotlight time" (time they get to actually do something at the game table).
Not everything has to be mission related or be a "subplot." They can just find out interesting things about the world they're in. If every story everyone ever tells them is a "subplot," then you get into a bad rut where their expectation is that anything that happens in the game world is FRAUGHT WITH MEANING, and it can't just be some guy BSing about how he fought a troll armed with a spoon once.
In my campaign, I make sure there's a healthy amount of "the world doesn't revolve around the PCs" stuff going on. Not only does it make for a realistic feel, but then when someone wants something to do, they have the expectation that "Hey, I can just go out there and go shopping, or find a bar, or find something to do - I don't have to be 'working through a plot element'" every damn minute of every damn day.
In my Pathfinder campaign recently, the party split. One half was going to do something on task and important. I don't even remember what it was and they probably don't either. The plan was to meet up at a known bar later that day. The other half of the party decided "we'll just go wait at the bar now." I roll a random encounter - giant cockroaches. They get to the bar, and the owner, "Ball-less Bill," an old ex-pirate with one leg, one hand, one eye, and apparently less then one thing down below, was standing outside the bar holding the door shut. "What's the problem?" "My basement flooded and there's these big ol' cockroaches running around in there! They're as big as dogs!" "We can take care of this! Stand aside, Bill!" The two PCs bust in and the cleric casts Call Lightning. The cockroaches are like CR 1/4, so they run all around and out into the street as the cleric blasts lightning holes in everything in sight. The fear of God is put into the local yokels, and the cleric gets an Infamy Point (the equivalent of a Hero Point in my pirate-oriented campaign). They yell "Wooo!" and go in and drink for free.
The other half of the party... They did something on mission. Got some information or something. Who cares. No one remembers that, but they remember the Great Roach Holocaust.
If you have proactive players, this shouldn't be a problem. If you have reactive players, then don't treat them like proactive players and give them 'things to follow up on.' Have the world turn, and its events happen around or to the players. If they decide to just go find another bar rather than chase out the giant cockroaches, fine, then make them choose whether they're drinking "bloodwine or dwarven grog" and go back to team A. Seems to me like you're overthinking this by requiring all events to be part of some big Mythic Plotweb.
Don't worry about it too much
Until you conspire with the first PC to backstab the party, they will stick together simply because they're the players. It's not perfect storywise, but it's often better than finding some elaborate explanation that breaks the flow of the game.
A larger evil
Have an enemy ready that catches them together at one point in the story. For this evil NPC (works best if he's a higher up, cult priest or sergeant or something), it's clear that the party conspires against him, that they are together. Fighting against him or just foiling his plans will make the party move closer together naturally.
Best Answer
One way for religion to matter, as you suggest, is for it to cause adventures. At a surface level, this is no more difficult that getting any other factor to cause adventures-- Give that factor power and the authority to hand out quests or obligations, and go from there. Even the narrow history and literature of western Europe presents several broad ideas:
At least two of those can be easily inverted such that the characters' culture is the object or target of the crusade or the missionary work. Really, almost any purely political motivation can be translated to a religious one without too much effort. These can also be made arbitrarily complex with faction complications.
A second very broad class of making religion matter, especially in a game with exploration themes, is to make some or much of the sense of wonder, or sense of exploration, revolve around religious differences. This comes with a steep cost in world-building effort, however-- you may need to design (and establish) not only a religion for your PCs' area, but for wherever they go to as well.
This does not cause adventures, per se, but it can certainly lend inflection to them.
And finally, if you really want any given factor in a game to matter, whether it be the weather or a religion, it should force the PCs to make difficult choices. This does not necessarily mean forcing impossible ethical choices on the characters, but it should mean making decisions that come with real short-term or long-term trade-offs and consequences: Do we break a local taboo in order to achieve a long-term goal? Do we break our taboo and possibly offend our own gods or our patrons back home? Our co-religionists over there are unfortunately in our way, but these unbelievers over here, have reasons for helping us-- do we accept? Those heretics over there just made us an offer we can't refuse... but really should; now what?
The key, if you want these decisions to matter, is to force the consequences to matter. Whether this is purely mechanical (you broke a taboo, your gods penalize you) or purely social or somewhere in between is possibly less important than the fact of real consequences, and consequences that are in some degree understood beforehand, and internally consistent to the setting.