Some investment funds will be forced to dispose of all or some of their shares in any form that drops out of the FTSE100. This might be thought to make the price fall. The same funds would buy shares (up to a determined volume) in any company that enters the FTSE100, and some people say the price rise due to this can be seen and played.
But I suspect all this is correct reasoning but the price implications for traders are too subtle to base buy/sell decisions on promotion/relegation.
Right now there are probably far more significant influences on the share price of an airline in the depths of a pandemic crisis.