Is it appropriate for a religious person to hand out brochures?

I think that that is vary wrong!!! I respect what people believe in but i would never try to force what i believe in on someone else. If i was in your situation i would just put all those papers in the garbage. Its one thing to ask someone what they believe in but it is really wrong to try and get them to believe what you want. Maybe next time tell the person politely that your company wont allow people to do that or ask her to not be so selfish and consider that other people have their own beliefs.