Are ripe meyer lemons supposed to be soft?
They should be quite a bit softer than a standard Eureka lemon, because the skin is much thinner. That said, it shouldn't be like a gentle squeeze causes your finger to sink in 1/2 an inch. If that happens, I think you've found a batch that are too old and have started to get mushy or lose moisture. Keep looking for good ones - Meyer lemons are terrifically fragrant, floral and mild.