GFCI trips when flipping light switch in another room
The old receptacle had more than 2 wires on it.  You presumed two of them were LINE, and got that part right.  However, if you look closer at the old receptacle, you can see that the two screws on the same side are connected by metal.  They are all LINE.  

You placed one or more of them on LOAD.  Move it back to LINE.  Most GFCIs have a feature that allows 2 wires to attach to one screw. 

As you know, the entire point of buying a GFCI is that it places the sockets in a "GFCI protected zone" where it will catch current leakage.  That side is called the LOAD side.   You can put other things there, but you must do that correctly and intending to do that.. The LOAD terminals are not extras.