It may be there are more serious issues than the screen doors potentially being an obstruction for residents fleeing a fire.
If the access doors are fire-rated then having screen doors installed may encourage residents to leave their fire doors open, rendering them useless.
And if you think that’s overstating the issue, check out this story from last year which shows the devastating effect of one door in one apartment being left open while the resident rescued his children from a fire. How bad was it? How about 19 dead and 32 hospitalised. If the door had been closed, most of those other residents would have survived.
Maybe your front door isn’t part of your fire protection. But if it is, then a screen door is both dangerous and redundant.