I hope the purpose of the announcement is not to accuse passengers of having their luggage in the wrong place, but rather to ask them to put it in the right place.
It's required that your luggage is under the seat in front of you"
means that the luggage should NOW be there. If it is not there the passenger has already not met the requirement, and it is rude for the airline employee to suggest that.
"It's required that your luggage be under the seat in front of you"
informs the passengers of the requirement that the luggage should SOON be there, and this is much more polite as it is asking the passenger to do something to meet the requirement (put the bag in the right place) rather than implicitly criticising him/her for not having already done it.
So, yes, I think the second is much more polite.
However the main problem applies to both versions. The requirement is not on the luggage to be or move anywhere, the requirement is on the passenger to put it there. So it would be much better to say
Passengers are required to place their luggage under the seat in front of them
or more politely
Passengers are requested to place their luggage under the seat in front of them
or better still
Ladies and gentlemen, please place your luggage under the seat in front of you
as this directly addresses the passengers rather than speaking about them, or their bags, in the third party.
BTW, Welcome to english.SE mattliu!
– laureapresa Feb 16 '16 at 05:35I do want to point out that @davidlol does raise an interesting question about Scalia's criticism of the original sentence.
– mattliu Feb 17 '16 at 19:28