Nope. Not really. There were some differences in cult and pantheon given that Sparta and Athens represented different Greek ethnic groups, but none of these differences are ever given as grounds for conflict. It was understood that every people worshipped the gods in their own way. Meanwhile, all Greeks honoured panhellenic sanctuaries such as the oracles at Delphi and Dodona and the temple of Zeus at Olympia; all Greeks observed the sacred truces that allowed for the proper celebration of the Olympian, Pythian, Isthmian and Nemean Games. Athenians and Spartans had this in common and never seem to have argued that their enemies did religion wrong.

It's not clear, then, why Apollo declared that he would fight on the Spartan side. There was little reason for the Delphic oracle to favour one over the other; both Athens and Sparta had a recent history of meddling with the sanctuary. Possibly the priests at Delphi realised that anything the god said would be interpreted as taking sides, and so they decided not to antagonise the side that was currently asking. But possibly they shared Sparta's concern over Athens' growing power, and worried that there might be Athenian plans to subject Phokis, the region in which the sanctuary was located.

This leads us into what the war was actually about, insofar as we can tell from the sources. I don't know where you read that it was mainly about commercial interests, but there's very little to show that this was the case. There was conflict between Athens and Corinth over spheres of influence, some of which were related to access to resources like timber, but this conflict was mostly expressed as a matter of prestige and political influence, not trade interests. Athens maintained a trade embargo against Megara to punish that state for abandoning its alliance with Athens, but Megara was not a big player in Aegean trade and there's no reason why the embargo would have affected Sparta commercially. Broadly speaking, Athens dominated trade between the Aegean, the Black Sea, and the Eastern Mediterranean; as an alliance of predominantly agricultural states, the Peloponnesian League was never a serious rival to that dominance and never really expressed any unhappiness with the trade situation. Bear in mind that the Greeks didn't really think about trade or the economy in the way we do. Their ideal was self-sufficiency, not unlimited growth.

Instead, all the conflicts and grievances that led to the start of the war were essentially about two things: autonomy and political prestige.

The first point is pretty simple: the Greek states valued the autonomy to make their own laws and decide on their own system of government, and the Athenians threatened that autonomy. The Athenian Empire, brought into existence to defend Greek autonomy against the Persians, evolved into a power bloc subjecting states to the interests of Athens and forcing them to pay tribute. Any attempt to break away from the Empire was ruthlessly suppressed. In its western and northern reaches, the Empire clashed with existing Corinthian spheres of influence, leading to local rebellions and a Corinthian desire to stop the Athenians once and for all. The Spartan rallying cry for the Peloponnesian War was that they would liberate the Greeks from Athenian oppression and give them back their autonomy.

Part of this question of autonomy was the fact that - broadly, though not everywhere and in all cases - the Peloponnesian War was a clash between two systems of government: democracy and oligarchy. The Athenian democracy had proven so successful that it had allowed Athens to grow into the new superpower in the Greek world, and many Greek states had embraced democratic systems of their own. But in the 450s BC the Athenians started actively imposing democracies on subject states under the assumption that democracies would be more favourably inclined toward them and their Empire. States where the oligarchic element was strong feared such regime change and flocked to oligarchic Sparta for support. In many cases the desire for autonomy was really a desire to overthrow or surpress democracy and to maintain the power of the old elite. The Spartans, like the Athenians, had a habit of forcibly installing the kind of government that was most likely to side with them - in their case, narrow oligarchy.

The second point is that the Greeks cared a lot about an abstract sense of interstate prestige and status. They ranked states, and demanded to be treated according to their perceived rank. During the Persian Wars, for instance, both Argos and Syracuse demanded the right to lead the anti-Persian alliance; when Sparta refused, arguing that they were the highest-ranking Greek state of all, the other two declared themselves neutral and left the alliance to its fate. You can imagine how this sort of ranking system would cause problems if a state were to suddenly become more powerful than it was before. Which states would have to make room for them? How would the old powers react to the new one? When Athens rose to prominence, first because of its key role in defeating Xerxes and then because of its Empire, it was clear to all that there would be trouble. First Corinth, and finally Sparta itself, took note of the rising star and went to war to assert that they still shone bigger and brighter.

It may seem silly to us now, but in a culture as obsessed with competition for honour as that of ancient Greece, concerns of prestige were enough in themselves to trigger wars, even without all the other causes for war that accumulated in the 430s BC. Thucydides' famous statement that the "truest cause" for the Peloponnesian War was Spartan fear of the growth of Athenian power must be read in this context, and not (as has been widely done recently) as a sort of Realist inevitability. Sparta feared that it would no longer be top dog, and they did what they could to reassert themselves on the Greek scene - leaving themselves with no serious rivals after their victory in 404 BC.