I was on Flight 91 from Tel Aviv to Newark this morning, when boarding a Chasidishe yingerman who was seated between 2 woman, asked the guy across the aisle who was sitting between 2 men if he minds to switch, problem solved without any noise or issues.
After take of a flight attendant came up to the person who agreed to switch and said: Thanks for being an Elite member (1k) are you Mr. ... Thank you for helping us and agreeing to switch, we would like to extend are gratitude by offering you either $250 or 12,000 miles to your account, which one would you prefer? I later asked the flight attendant what it was all about, she said that we have a program to compensate passengers who help us during the flight.
I would suggest to ELAL instead of threatening religious passengers who dont want to sit next to woman by removing them from the flight , just try to be creative and find a way that passengers shouldn't mind switching when needed.
It might add a bit to their overall operational costs, but i believe it will still be cheaper than the ongoing PR nightmare, and loss of religious passengers who feel betrayed by the airline not respecting their beliefs.