Electrical - GFCI tripping
Because "continuing the circuit" is a completely different thing than "placing a load inside the GFCI's protected zone". Especially where switches are present!

I get it. You've installed receptacles for decades.  You know (other than split receptacles) the extra 2 screws on the receptacle are for continuing the circuit onward.

Now you also know there are some receptacles (eg. USB) that only have 2 supply terminal screws.  They do not provide any method for continuing the circuit onward.  With those, you are forced to pigtail the receptacle and use a wirenut to splice its supply with the onward wires.  

GFCIs are like that too, GFCIs only have two supply screws.  They are conspicuously marked LINE and they are the only terminals not covered with warning tape.  (The warning tape says, in so many words, "For Wizards Only".)So, similar to a USB, these should be pigtailed with a wirenut for continuing the circuit onward.  Only the LINE terminals should be used.  This is especially true in a retrofit situation like this, and double especially when there is a switch in the same box.

Everything I have said so far is about continuing a circuit onward, which is what you are trying to do.   Now we're going to turn the page. 



GFCi devices come in several packaging styles.  There,s the GFCI+breaker, the plain GFCI deadfront, and our friend the GFCI+receptacle.  All of them provide a "GFCI protected zone".  Obviously, on a GFCI+receptacle, the protected zone is the built-in sockets.  

However, all of them can extend their zone of protection beyond the device itself. (That'd be kinda necessary on the breaker and deadfront, eh!?)  How to do that is beyond the scope of this answer.  But you may know a rule that currents must be equal in any cable.   That rule applies in spades to any GFCI zone of protection.  This makes it rather tricky to work with them in switch boxes. 

However there's generally no value or benefit to putting hardwired bathroom lights, fan, heater etc. on a GFCI. 



Bottom line, pigtail everything to LINE and call it good.