If you consider “complicated” to mean “a majority of Muslims believe homosexuality should be punishable by death” and an even larger majority believe at that very least it should be illegal then yes, it’s a complicated relationship.
In Great Britain, home of the most “progressive” Muslims in the world, 61% want gays to be “punished” and only 18% think it should be legal.
This is not a condemnation of all Muslims. These numbers are simply a piece of a larger picture that clearly illustrates that the majority of Muslims are incompatible with Western culture. Pretending that a problem doesn’t exist does not make one righteous, it makes one a damned fool.