Just finished a job where HO wanted 2 prong outlets replaced with 3 prong ones. House was built in 1954 and there was no ground wire in the romex.
We installed GFI recept's on the first outlet in each circuit and put the GFI protected No Equipment ground stickers on all the new receptacles we put in. The refrigerator is the last outlet on one of the living room recept circuits.
Plugging in the refrigerator causes the GFI to trip immediately. Plugging it in to another circuit trips that circuit's GFI immediately. We connected drills, lamps, and a heat gun to both of these circuits and they all worked fine.
My problem is convincing the HO that his refrigerator has a problem. I told him we could put GFI recepts in each outlet on the circuit with the fridge so it would not be GFI protected, but that it would not be safe as far as him (or his renter) not getting shocked. He thinks I should do this for free since the fridge worked fine before the GFI's went in.
I'm thinking I'm not going to do it at all until we plug the fridge into a non-GFI protected outlet, wet his concrete floor, and he grabs the fridge while he's barefoot. Just kidding about that part, but not about the not doing it part.
Any reasons I'm unaware of that the fridge would trip a GFI.
There is no continuity between the ground prong on the fridge cord and either hot or neutral prong.w
Make sure that you do not have a reversed polarity in the circuit somewhere, many times I have run into where old non-grounded circuits that had the cloth covered rubber insulation it was very hard to tell which wire was the hot or the neutral, especially at the lights where the heat from over lamping the fixture would bake the color out of the conductors, someone comes along as installs a new fixture and pulls apart the conductors but doesn't remark them and the hot and neutral gets switched, while this shouldn't cause this problem but if you bootlegged the ground terminal off the neutral or what you thought was the neutral then now the ground prong on the receptacle is hot in reference to earth so the case of the appliance is hot and since it is making connection to a concrete floor the GFCI does what it is supposed to do trip the GFCI.
Because you stated that you measured no continuity between the ground prong and the hot or neutral on the cord of the appliance then I suspect that the ground prong on the receptacle would have to be giving reference to another conductor, even using a GFCI you are not allowed to bootleg the ground to the neutral and is a very dangerous mistake to make, if the neutral and hot are swapped ahead of this receptacle you would not know it as AC doesn't care if only two conductors are referenced it will still show correct polarity, now if you run an extension cord to a truly grounded receptacle that maybe is close to the panel that can be verified at the panel or even temporally install a receptacle off the panel to use as a test reference, then plug in a long enough extension cord to reach the receptacles in question so you can use it as a reference to check which conductor is the true hot and which is the true neutral, verify if the neutral and hot has not been reversed, this and only this is the best way to make sure you are not going to have a dangerous problem after you do an update like this.
Also make sure you or your workers did not bootleg the ground prong to the neutral at this or any receptacles, even using a GFCI will not make this a safe installation and is a very big code violation that some thing is allowed if the GFCI is used, I have electricians even think this was allowed even when a GFCI is not used.
I had a service call to a house that an elderly lady was getting shocked if she touched the freezer in her garage, about a month before I was called she had a friend run a circuit to the garage to feed this freezer, the house had old cloth UN-grounded type circuits and he ran the new NM to a receptacle in the crawl space that was for the sump pump, he had mistakingly reversed the polarity of the old cloth covered wire on this receptacle then bootlegged the ground to what he thought was the neutral at the sump pump receptacle, after checking with an extension cord to a receptacle I pig tailed into the panel to make sure I had a good reference point, I found that the freezer had 120 volts on its case, upon checking the receptacle both the neutral and the ground pins both were hot, I removed the receptacle to find it wired correctly, but the ground and neutral wire was still hot and the hot showed as a neutral, I traced the new NM into the crawl space to this pump receptacle after pulling it apart I saw what had happened, he had unknowingly reversed the hot and neutral when he tied this new NM into the old conductors, he had connected the EGC, and the new neutral to what he thought was the neutral in the old NM, I even had a hard time telling which one was which but the extension cord made it very clear.
The problem with this vary dangerous mistake is that the GFCI or a 3-light plug tester can not tell you that you have a reversed polarity if the EGC or ground prong on the receptacle is also bonded to the neutral at the receptacle, it will light up the lights that show the receptacle is correctly wired, but the danger just sits there in wait for a person to make contact with this hot EGC and a true path to another grounded appliance or Earth like the concrete floor.
So I would go back and run the test using the extension cord to a known good reference receptacle or if you don't have one pig tail one into the panel temporally, then check this circuit with a voltage tester from the ground pin or the neutral pin to the suspect neutral to see if it shows hot, if so find where the neutral and ground has been reversed, other wise if someone was to get hurt you could be found liable even if it was reversed before you touched anything, also never bootleg the ground pin off the neutral even when using a GFCI, because if the neutral was ever lost it can cause any appliance that is plugged into any receptacle wired like this that has a grounding type plug that grounds the case of that appliance to be hot to earth even if the circuit has the correct polarity, this is why we never are allowed to do this.
Also I should add tht the reason I suspected the bootleg ground to neutral was that you made the statment that you checked the continuity to th eground pin on the fridgorators plug, if these is no wires connecting to the ground terminal at the receptacle then a referance of the ground pin on the fridges plug is meaning less.
Also keep in mind that it takes an impedance of 20k to 25k ohms or less to trip a GFCI most common continuity testers will only show continuity if the impedance is lower then 1k ohms, some even less, so a leakage could get over looked, using a megger would be the best way to test this.