Certainly. In fact there was even a whole series of Sacred Wars.
More specifically, the First Sacred War was fought by the Amphictyonic League against the city of Cirrha over the latter's mistreatment of religious pilgrims to Delphi. Delphi derived religious significance from its Temple of Apollo, which housed the famous Pythia - the Oracle of Delphi.
The Amphictyonic League was an ancient religious organisation which formed to support the temples of Apollo and Demeter at Delphi and Anthele.
The Amphictyons (literally, “dwellers around”), or Amphictyonic League, oversaw the oracle of Apollo at Delphi and had the power to declare wars (called Sacred Wars) against those guilty of sacrilege.
- Phillips, David D. Athenian Political Oratory: 16 Key Speeches. Psychology Press, 2004.
Pilgrims from all over Greece came to Delphi to seek answers from the priestess, the most prestigious of her kind in the classical world. Many of them would disembark at Cirrha, the closest port to Delphi. The city took advantage of this to impose a toll on pilgrims, a sacrilegious act that ultimately provoked a war with the Amphictyonic League.
Delphi was situated at the foot of Mount Parnassus, and visitors to the shrine who came from any part of Greece by sea usually landed at Cirrha, a seaport town on the north shore of the Gulf of Corinth, which happened to be the nearest port to the oracles ... The men of Cirrha were in the habit of extorting heavy dues from travellers on their way to Delphi, and as they would not abandon their exactions at the order of the Amphictyons, these representatives of the Greek states ordered war to be undertaken against them.
- Robinson, John. Ancient History: A Synopsis of the Rise, Progress, Decline and Fall of the States and Nations of Antiquity. London, 1821.
Not only did the war began with a distinctively religious cause, it also ended on a religious note as the lands of Cirrha were made sacred.
The First Sacred War was subsequently fought, resulting in the destruction of Cirrha. The plain around Cirrha was then dedicated to Delphi and cultivation of the land was forbidden.
- Ashley, James R. The Macedonian Empire: the Era of Warfare Under Philip II and Alexander the Great, 359-323 BC. McFarland, 2004.
This affair is actually somewhat similar to the later Crusades of Christendom:
The Amphictyonic league at length - under pressure, it is said, from Solon - proclaimed a kind of holy war against the Cirrhaeans, something like the crusade undertaken to free Christian pilgrims from the tax levied by the Saracens at the gates of Jerusalem.
- Shuckburgh, Evelyn S. A Short History of the Greeks: From the Earliest Times to BC 146. Cambridge University Press, 2013.
As @Matt pointed out in the comments, so-called religious wars in history were almost always also motivated by economical and political concerns. The First Sacred War is no exception here.