Here are a few options, depending on where you want the focus to be:
Option 1 (Direct and professional):
Developer of Fox River Resort Refutes Rumors of Exclusive Resort Policy
Option 2 (More formal/Journalistic):
Fox River Resort Developer Denies Allegations Regarding Religious Exclusivity
Option 3 (Concise):
Fox River Resort Developer Dismisses Claims of Religious-Only Development
Note: In a formal headline, it is generally preferred to use “refutes,” “denies,” or “dismisses” rather than “calls a lie,” as these words maintain an objective, journalistic tone.