Well, fortunately, the OP is simply asking about using a phrase in conversation with one person (with whom she is friendly) in a social context (that happens to be in a place of employment because they work together), rather than in a workplace presentation or official meetings. I don't think she wants to use it as her email signature or anything, and she's not blessing you or anyone else non-religious.
It's fine for a person to be religious or not, it's not fine to impose your preferences and expect others to suppress aspects of their identity in their own interactions with people who are their friends, even in the workplace.
I don't think anyone here is looking to impose their own protected characteristics on other people. People are saying to the OP that saying "God bless" to someone who is a practising member of another, closely connected faith is unlikely to cause offence. That's not the same as suggesting it as a universal greeting. People are also saying that it's not realistic to expect people to entirely suppress major parts of who they are.
What would 'keeping religion out of the workplace' look like to you? Because if it means people being prevented from reasonable adjustments such as dressing in accordance with their faith/culture, people being told they cannot use any language referencing religion even in their more private interactions with their peers (tricky if, eg, someone's first language is Arabic, because so many phrases are connected to words with relations to faith), people being told what they can and cannot do in their own breaks, etc., then that's going to go down like a lead balloon with HR and lead to a recruitment and retention difficulty.
This isn't an AIBU about workplace conduct. It's a thread in the Muslim Mumsnetters board started by a practising member of a different faith to ask about a specific situation.