Depends on your jurisdiction, what you described sounds like a labour dispute in a very employee hostile place. Where I live it's illegal to fire people who threaten to strike
Sadly, fighting strikes and unions has probably become an art at this point.
The law has evolved to help balance the relationship between employer and employee. It dictates limits on employer behaviour and also limits on employee behaviour. Usually there is a formal structure (union) to act as the employee representative.
None of which is in play here. There are no employees, just volunteers. There is no union. Yhe action appears to be somewhat arbitrary. Why private groups? Why 48 hours? Has there been any formal discussions to the root dispute? Is there a union for API users? What link us there between API users and moderators?
So yes, the response seems heavy-handed, but the proposed action seems premature. The mods are testing their power and Reddit is responding. And there's no law governing any of this, on either side.
They have basically reached the monetization phase, where most smart users bail either just before or shortly after. You get the same dynamics with tyrants, only you have more risks and more options available to you in the real.