I've had players like this, and my experience was
1. Ignore, hope it goes away
2. Speak to player privately
3. Ask player publicly to participate
4. Ended player's participation
Now that was only for an individual. If the majority or all the players took the stance you describe, I'd likely swap out the game for one more conducive to the players' style.
Now all of the above is based on the OP's depiction of the players' attitudes: Neutral alignments, playing very mercenary style PCs, motivated entirely by rewards. I don't think any of my advice helps them work as a team.
The 2 might be linked though by a simple reward-based system, but it ends up being highly subjective so a lot of players might feel condescended to. Basically you have some big tokens, like medals or poker chips. Every time the party acts as a team they get a token. These can be redeemed that game session for some big boost, like a +2 for all party members for a minute or a mass-invisibility for a round or whatever. The catches are: they can never have more than 3 at one time and all tokens must be redeemed in THAT game session.
See the thing is: some players DON'T want to be good. They want to be an antihero, or not even a hero at all. For these kinds of players, playing a heroic, story-driven game is simply frustrating for everyone.
I have a group of gamers. I wouldn't say they're not heroic, but they're definitely not motivated by anything IN-game. They are powergamers plain and simple and enjoy killing monsters and getting treasure. Their characters tend to be very 2-dimensional and the stories we create are highly limited - my plots could usually be summed up in a paragraph.
Now for years I made epic campaigns and tried to force my players to engage in them but the reality was the players never cared about whether the NPCs lived or died, or what the BBEG's motivations were, or any of the other RP elements of the game. For these guys the game is simple: we show up every month, roll some dice and beat the crud out of some baddies.
I finally gave in and made up a homebrewed megadungeon contained inside of a sandbox region of my world. The players can LITERALLY have any game they want. I have complex social and RP situations at the ready, but I have little actual plot other than what the players pursue.
So far they've entered the megadungeon, found out there's a kobold sadist BBEG, an NPC got mad at said BBEG and vowed revenge, and then the party accepted a side quest ending a local curse. From here they might help the NPC, they might wander the dungeon on their own, they might just head into surrounding hexes and see what's around them.
The point is: my players are highly independent thinkers who don't enjoy RP. Rather than force them to work as a team for the common good and embroil them in a twisted plot they don't care about, I've instead given them such a blank slate that they need to seek out their own motivations. My hope is that they'll trip and fall into the role of heroes on their own.