They do not have a right to question them. But they do have a right to decline to provide a service which is against their religious beliefs.
To steal a few lines from Krauthammer's latest column:
Catholic soup kitchens do not demand religious IDs from either the hungry they feed or the custodians they employ. Catholic charities and hospitals — even Catholic schools — do not turn away Hindu or Jew.
Just like Muslims restaurants don't serve pork and Hindu restaurants don't serve beef, Catholic organizations don't provide contraception or abortions.
“They have the right to decline to provde a service which is against their religious beliefs.”
Yes, and this is why Obama responded to the hue and cry by transfering the responsibility for providing these services to the employees’ insurance companies rather than to the hospitals themselves.