If a Muslim lady works with non-Muslims, can she call the males as her brother out of respect.
Does Islam give her permission to do so?
There is no problem in calling a non-Muslim by my brother's word.
exactly the contrary,
it's respectful and appreciated to calling a non-muslim by my brother's word or sir, etc..
and be friendly with him to give him a good picture of the Muslims.
that is what Allah Almighty ordered us to do.
Evidence of this in Surat ((17) Al-'Isra') Chapter number [17.53].
" Tell My worshipers, that they should say words that are the finest ".
In Arabic: (سورة الإسراء الآية رقم 53)
"وَقُلْ لِعِبَادِي يَقُولُوا الَّتِي هِيَ أَحْسَنُ"
But on the condition, that doesn't exceed the limits stipulated in Islam, between the girl and the non-mahram whether he is a Muslim or not.
call non-muslim or Muslim by my brother's word it's just word to express the respect and appreciation. and don't cancel the sanctity(Hourma) between of the girl and non-mahram from men.
I hope my answer is clear.