If it was me, I'd buy off-the-shelf explosive gas detectors (which already commonly exist) and when they went off instead of sounding an alarm I'd release nitrogen or argon gas. Both are inert or inert for all intents and purposes (as with nitrogen).

Inert gases are already used in fire suppression systems. Even if the flammable gas was still flammable when mixed with our almost inert gases, its would still likely slow down the burn and reduces pressure within the ATM/cash point.

However there is likely a realistic limit on how much gas you'd store in the ATM, so they could trick the system into pre-firing, wait a few minutes, and then try again. So you'd likely want to set off the building's alarms to stop such an attack vector (even assuming a 10 minute police response, they likely cannot try the attack twice).

I was thinking along those lines too. A 46" high nitrogen tank holds around 125 cubic feet. As a wild guess, if an ATM contains 5 cubic feet of air then you could completely change the air 25 times with one tank. Does that sound reasonable?

You don't really need to stop the explosion so much as make it not worth the thieves' while. Just spray the money with indelible die as soon as you detect the gas. You may lose a few ATMs this way, but the thieves will pretty rapidly give up on those from any bank that widely deploys such a device.

Wouldn't a simple solution simply be a vent? Constantly vent out all the air in the machine. Seems a lot more effective than trying to build bomb proof hardware...

How about just using a fan? Make the whole machine positive pressure and I don't think you could get enough mix into the chamber for long enough to get a blast.

Something that would hit all of these fuel-air explosive mixtures would be an oxygen scavenger, which would also likely make the electrical and mechanical stuff inside the machine happier.

Not sure how practical that would be. Another scheme would be one or more sensors detecting an attack triggering the release of a lot of CO2 to keep the fuel-oxygen mixture in the machine at a minimum.

One defence could be to detect the gasses and to stain the cash with exploding dye packs, so if the thieves destroy the ATM and grab the money it is permanently marked and traceable back to them.