Assuming these are informal jams, you just don't have the authority to fire incompetents.
I think the only possibility is to endure the fact that the material will not be played correctly.
But do at least point out what "swing" means when they try to "correct" those who are playing it correctly.
Is it tactless to teach someone the truth?
music.stackexchange.com/users/18664/Andy
The only way I am aware of improving (or practicing) swing feel is to play with a metronome but set it so the click is on the 2 and 4.
Emily Remler goes through it in her tutorial videos.
I have no idea how this would translate to a group jam though!
music.stackexchange.com/users/953/Robben_Ford_Fan_boy
If you're playing straight and switch to playing swing, the 'and's move but the strong beats don't.
It might be that the players who are trying to play swung are pushing the strong beats around too, which would be disconcerting to the other players.
I'd suggest an exercise where everyone plays the same line (a fragment of a scale for instance)
first straight and then again swung.
You can also try clapping exercises like this, where you silently count the lower-case and then CLAP the upper case: one-and two-and three-and four-CLAP
The 'ands' and the CLAP move around depending on whether your quavers are swung or not.
The other thing I tell my beginner brass band when they're playing swung quavers is to make the first note in each pair long, and to make gaps between all notes as short as they can, whilst still articulating every note and not slurring it.
Without this reminder, the tendency is to play the first note of each pair too short - and the result is a very 'polite' performance.
Once you lengthen the first note in each pair the performance has far more attitude and sounds much jazzier.
music.stackexchange.com/users/9426/Brian THOMAS
Honestly you should bring in some tennis balls and make a game out of it.
I've taught this with eurhythmics before.
Basically have people walk to a beat and start bouncing the ball on the 8th note, and then after they do that comfortably have them do the same, only swing it.
You can work with whatever rhythms you need in this way
and it feels kind of silly at first but in general it's really fun and people tend to get into it once they're over the silliness.
You can also do it with 2 people where they alternate beats and then bounce the ball to each other for the swing.
A little unusual but it works and they use this stuff to teach really young kids about rhythm, so older people shouldn't have a problem with it.
music.stackexchange.com/users/30965/Tam Hartman
The best way I've found is to have a solid rhythm section that knows what to do.
Primarily the drummer.
If he plays a swing rhythm, basically on hi-hat/cymbals, that sets the groove.
As a bass player will be playing on the beats more than the offbeats, he won't swing until he puts something like ghost notes on the offbeats as well.
But not constantly.
The guitarist will help, as his upstrums will either be in a straight 8 or swing feel.
Working together to produce this, the other players usually get pulled along into that swing (or any other) feel.
Interestingly, a lot of the late '50s, early '60s pop music had something like the feel your band has.
The older players preferred to swing, while the young upstart guitarists wanted to play straight.
It can be heard on some of the early Elvis tracks.
music.stackexchange.com/users/2808/Tim
In a couple of jams I've been in recently there are players who play swing and jazz music but who play it as straight-eighths.  Worse, they try to correct the other players who are swinging the beat because they hear it as unsteady.  What is a relatively tactful way of teaching these players how to swing in a group setting?
Teaching others how to swing
music.stackexchange.com
<rhythm><jazz><jamming><swing>
music.stackexchange.com/questions/46453
music.stackexchange.com/users/10635/pro
The best way to teach people how to swing is to have a solid rhythm section that knows what to do, especially the drummer. If he plays a swing rhythm, basically on hi-hat/cymbals, that sets the groove.  As a bass player will be playing on the beats more than the offbeats, he won't swing until he puts something like ghost notes on the offbeats as well. The guitarist will help, as his upstrums will either be in a straight 8 or swing feel. Working together to produce this, the other players usually get pulled along into that swing (or any other) feel. Drummer, guitarist, bassist and guitarist need to work together to produce a swing rhythm
Drummer, guitarist, bassist and guitarist need to work together to produce a swing rhythm. Older players preferred to swing, while young upstart guitarists wanted to play straight. A lot of late '50s, early '60s pop music had something like the feel your band has. It can be heard on some of the early Elvis tracks. The swing feel can also be found on some early Elvis songs, including "I Want You Back"