Sump Pump Trips GFCI Receptacle. Is a single, dedicated non-GFCI receptacle safe?
There used to be an exception to the code, that said that a sump pump didn't have to be on a GFCI if it was on a dedicated circuit, and it was connected using a single receptacle*.  And by "single receptacle" they meant a non-duplex receptacle.  One like this...



With that said, "officially" there should be no problem with having a sump pump on a GFCI circuit.  Unofficially, there are sometimes problems with sump pumps on GFCI circuits.  The manufacturers are supposed to reduce or eliminate any leakage current, However, nobody sent the memo to manufacturers so they don't always get it right. Because of this, you may find that a sump pump does trip a GFCI from time to time.

If the GFCI was tripping every time, and immediately. You'll want to first verify that:


There is not a ground-fault in the sump pump.
The GFCI wiring is correct.
The GFCI is not faulty.
The GFCI was manufactured within the past 3-4 years.
The GFCI is rated for the proper current draw.
The circuit wiring is correct.


If all of this checks out, you may wan to consider using a single receptacle to connect the sump pump.  While it's not up to code, a slight electric shock hazard may be preferable to a flooded house. Though a house flooded with electrified water, might not be the best thing ever.

WARNING:

It is not safe, or up to current code to install a sump pump using a non-GFCI receptacle. And I am not telling you to do so.

I will say that a sump pump installation does not require the circuit to which the pump is connected to be upgraded, if the pump is connected to the circuit in a cord and plug configuration.  

**citation needed*