Permissibility of greeting non-Mahram women if there is no fear of temptation
5-3-2017 | IslamWeb
Question:
Assalaamo alaykum Scholars. The shaykh I usually ask for fatwas told me that greeting non-Mahram (permanently unmarriageable) women is haram. I apply that, praise be to Allaah, and if they are muslims I do not care, but there are certain people whom I have tried to avoid greeting, but it has been really diffiuclt. This is when I encounter my teacher in a one way road, so I cannot pretend to not have seen her, so I feel shy not to greet her. Actually, in most cases, I do not even speak; I subtly lower my gaze and subtly raise my hand and smile , so in most cases I do not even speak. Notice that with Muslims females, I do not care; I do not speak to them, nor do I greet them, nothing. However, as I said, with my teachers in university, I feel quite shy to pass in front of them and ignore them. Is what I do permisible?
Answer:
All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad 
is His slave and Messenger.
Many scholars are of the view that it is forbidden for a man to greet young non-Mahram women with the Salaam because of the fear of being tempted by them, but not women who are of advanced age.
An-Nawawi 
said:
“With regard to a non-Mahram … if she is an old woman who is not desired, then it is recommended for him to say Salaam to her (greet her), and it is recommended for her to say Salaam to him. If either of them greets the other with Salaam, then it is an obligation on the other to respond. But if it is a young woman or an old woman who is desired, then a non-Mahram man does not greet her with Salaam, and she does not greet him either. If either of them greets the other, they do not deserve to be responded to.”
Some other scholars permitted this in regard to all women, provided that one is safe from being tempted by them.
Ibn Battaal quoting Al-Muhallab said, “Men greeting women with Salaam and vice-versa is permissible if there is no fear of temptation.”
Ibn Hajar mentioned this in Fat-h Al-Baari.
Accordingly, if you are safe from being tempted by them, then there is no harm on you in greeting them.
Allah knows best.