Meet Charlie. Charlie is a devout Catholic and has a 10 hour layover in Narnia Airport. He decides that he will go and have a bit of restorative prayer at the Christian chapel provided.
Now meet Dan, a devout Muslim who has a 15 hour layover. He is saddened to find there is no area set up for Muslim prayers so he is unable to say any of his Salah prayers.
Has Dan been treated less favourably by the airport and unlawfully discriminated against?
Not offering a particular service is not a crime and also not discrimination. In the example stated, the "particular service" would be "prayer room for Muslims".
The example provided is not optimal, since airport chapels are normally arranged so that people of every religion find what they need (e.g. they provide the Koran as well as the Bible). Of course, it's possible that Dan arrives just when there's a Christian service in the chapel, but then he can just wait for half an hour or so.
In the general case, no private entity is forced to offer a particular service. So even the airport would not be forced to offer a prayer room, let alone a Muslim prayer room. It could however be illegal discrimination if Dan wasn't allowed to enter a Christian chapel because he is Muslim. This is the same as if the waiter in a restaurant denies entry to black people (a serious crime in many countries). But it's of course legal for the waiter to not (specifically) offer food for Muslims (e.g. without pig).
It depends on the extent to which any chapel is provided. Under 42 USC 2000a, it is illegal to discriminate on the basis of religion in a place of public accommodation. An airport could set aside a room for vague "quiet contemplation", but it could not specifically limit the use to Catholic prayers or Buddhist meditation. Illegal discrimination is not just based on a filter "If Muslim, no entry", it also includes practices with discriminatory effects. If a seemingly-neutral facility is closed during the times for Muslim prayers, that would be clearly discriminatory. A legally untested question is whether a facility could get in legal trouble if it does not provide male-only and female-only prayer facilities, given the premise (by some in Islam) that men and women should not pray together, likewise in Judaism (note that sex discrimination in public accommodations is allowed).
