Given this only seems to be afflicting MAX8 craft in terms of material evidence, my guess is they won’t ground the whole series unless/until another MAX craft goes down.
AFAIK the avionics on both variants are the same. A pilot who is (properly!) trained and type-rated on one should be able to effortlessly use the other.
The only difference, again AFAIK, is the passenger and cargo capacity, length, and the range.
The 737 type rating (training/licence addon required) covers pretty much the entire family of 737s from the 200 to the max.
The avionics are the same but because the planes have substantially different air-frames, the software parameters and possibly some functionality will differ. It's not unreasonable for differences in these flight parameters to be a factor.
Honestly, it goes even further than that. The generally accepted theory in the Lion Air incident is that a system caused MCAS might be one of the major causes of the accident.
Basically, the larger/more powerful/further forward engines on the MAX would cause the airplane to behave differently to other 737 variants in some situations, and MCAS is designed augment pilot input and allow the pilots to fly the planes as they would have flown other 737s (and allows pilots to fly MAXes under the same type ratings as previous 737 models). However, in edge cases (in the case of Lion Air, erroneous sensor input) the airplane might do something totally different from other 737 variants. Evidently Boeing didn't even require pilots to be told about MCAS, because all it (supposedly) does is make a MAX feel like an older 737.
