In Upper Germany, people greet each other by saying "Grüß Gott". It has the same function as English "good morning".
This greeting means "God greets you", however, nowadays it has mostly non-religious meaning. People say "Grüß Gott" no matter if they are members of any religion or not. I am an atheist and I use that greeting too, as everyone else.
I am not sure if I should use "Grüß Gott" toward Muslim people. Regions where "Grüß Gott" is used are fulfilled with vast majority of Catholic religion. Maybe for a Muslim person "Grüß Gott" may sound as "my God greets you", which may be not nice for him/her? The Bible says, that "the God is only one". Thus, can be "Grüß Gott" even offensive?
Where I live, people all around say "Grüß Gott" toward Muslims, since it's the culture of that region. However, if this greeting is not something nice for Muslim people, I would want to respect them and use some other greeting.
Maybe is there any person living in that area who can tell his/her thoughts about that topic?