Maximum Allowed inrush current in Eurpoe
First, there are 2 different specs on any circuit breaker: "thermal" limit and "electromagnetic" limit. The first one is typically set to 16 A. It limits continuous consumption currents. The second one is much higher (100 A or more) and it works very fast. It protects against short circuits or too high inrush currents.

So my advise is:


Design your circuit for inrush peak current of 100 A during few ms.
This huge current is not the one you measure - you just clamp it.
The real measurement range can be 0 - 2 A or a little higher.


I guess you use current transformer for measurements, so just limit the voltage on the secondary winding load. The limiter must carry large enough current in "peak" mode (not continuous).

By the way - most low power electronic devices use thermistors to limit inrush currents. So the same device shows very different inrush currents depending on ambient temperature and the time since last switch on event.