When your response to a reasonable request by an authority figure is to reject it and start ranting about some nonexistent "rights", you are looking to cause a scene. This woman got her wish.
Well, let's assume for a moment that she didn't 'rant'; Let's say she just 'replied'.
If a vegetarian flight attendant told you to stop eating that SlimJim in her presence, you'd be well within your rights to tell her no.
I wouldn't stick an airline blanket on my toddler's head either, any more than I would encourage her to eat things she finds on the floor. Gross.
Apparently it is a right codified in the laws of the state where the airplane had landed, so it is not non-existent.