The Shrine is the only one that I know of. There have been instances of conflicts between the Shrine and Grand Lodges in the past. To my knowledge, except in one instance, these have all been resolved.
Small versions of that conflict seem to happen in some state or another every couple of years. All of the past ones have blown over in under a year, except that one.
I do not know of any other organizations that have had conflicts with Grand Lodges. If I am wrong please provide some examples with credible sources.
Some of them are not nearly as spectacular. Jobs Daughters can not operate in Texas for example. Some conflict about background checks and putting practices about them in place before a deadline.