It was a mixed bag, but generally: no, not really. Writing about 500 years after the events in question, Plutarch comments on exactly this in his Life of Artaxerxes. Though he was writing much later, and moralizes to blame Spartan failure against Thebes at Leuctra on Persian effeminacy, it is unlikely that Plutarch invented this. When the Spartan ambassador Antalcidas returned home with gifts and souvenirs from his time with the Persian court, people openly mocked the Spartans for it, and the Spartan King Agesilaus had a witty response at the ready:

But Antalcidas was a fit person, as it would seem, to be exquisitely treated and to receive such a wreath, now that he had danced away among the Persians the fair fame of Leonidas and Callicratidas. For Agesilaus, as it would appear, when someone said to him: "Alas for Greece, now that the Spartans are medizing," replied, "Are not the Medes the rather spartanizing?" However, the wittiness of the speech could not remove the shame of the deed, and the Spartans lost their supremacy in the disastrous battle of Leuctra.

However, this discourse came long after Sparta's victory in the Peloponnesian War, and only started circulating after their repeated defeats in the Corinthian and Boeotian Wars. At the height of their own hegemony, nobody could really dispute the effectiveness of Sparta's alliance with the Persians. That brings me to something I'd like to dispute in your original question:

Sparta sought help from the Persians in order to beat Athens, which they did, but only in a Pyrrhic victory.

Sparta sought and received aid from Persia on two occasions: once at the height of the (Second) Peloponnesian War and again near the end of the Corinthian War. The latter was certainly a pyrrhic victory in that Sparta's power was greatly diminished while the rest of Greece was able to build back up and challenge them again 15 years later for the Boeotian War. Though, as a Persia specialist, I'd argue that it was a pyrrhic victory for all of Greece because both sides were forced to submit to terms from Artaxerxes II and tried to justify all of their actions to the terms of that treaty for decades. However, the first time led to Sparta's uncontested dominance among the Greeks for a decade, in the mainland peninsulas, in the colony cities of Thrace, and even to a degree among the islands and Anatolian cities under Persian control.

More to the point: Why didn't the rest of Greece more aggressively accuse Sparta of medizing when they were powerful? Because the rest of Greece was doing the exact same thing.

The Persians were the biggest threat.

By the Peloponnesian War, this simply wasn't true. The Delian League wars against Persia from 477-465 BCE had effectively wiped out Persia's naval dominance in the region, and Athens had both conquered Persian territory and plunged deep into Egypt in support of a local rebel. In 449, Artaxerxes I agreed to the Peace of Callias, officially granting Athens control over the Greek cities claimed by Persia and promising to keep Persian forces away from Athenian territory in exchange for an end of hostilities. Any lingering fear of a Persian invasion was a purely Greek rhetorical device.

Even though the Peloponnesian War was ongoing, Persia ultimately entered its own war with Athens independently when the Athenians formally broke the treaty by providing direct aid to a rebel governor in Caria. Darius II authorized the Satraps of Lydia and Phrygia to retake their coastline from Athens. Neither had the authority to call up a navy from other provinces, and Darius was reluctant to send in the Persian fleet while Athens remained a threat at sea.

Lucky for them, this order happened to coincide Athens' disastrous defeat in Sicily, wiping out much of the Athenian fleet in 413 BCE. The loss sparked rebellions in Delian League cities, some reaching out to Sparta, others to Persia. It also gave some room for the Peloponnesian League and Persian satraps to start building up fleets of their own without Athenian attacks on their shipyards. Under that context, the Satraps of Lydia and Phrygia reached out to Sparta, not the other way around. Sparta had sought Persian financial aid before, but nothing came of it. Now the Satraps wanted to initiate a formal alliance with the Spartans as common enemies of Athens. They would provide the money and the army on land. The Peloponnesian League would provide the ships, sailors, and marines.

Almost immediately, the Persians were in constant negotiation with Athens, contemplating shifting their support to the other side of the war in exchange for immediate control of the coastline. The Greek historian Thucydides lays this two-timing squarely at the feet of the Athenian general in exile, Alcibiades. Modern historians give more credit to the Persians themselves, interpreting these negotiations as a delaying tactic to damage both Greek powers so that neither would remain a threat to Persian interests. Athens remained in open negotiations trying to win the Persians over for five years, with the Persian willingness shifting back and forth depending on how well the Spartan fleet was doing at the time.

By 408, the Spartans themselves were sick of it and sent an embassy to the Persian royal court to negotiate with Darius II, correctly suspecting that his official reports weren't reflecting reality in the Aegean. That prompted more direct royal intervention in the form of Cyrus the Younger, the 17 year old prince who was given full control over the Anatolian satrapies and a mandate to wrap up this war by beating Athens. That came to fruition in 404, and Cyrus had forged a strong and apparently lasting alliance with Sparta. After a failed bid to usurp his brother's succession rights, Cyrus returned and received aid from Sparta in a conflict with one of his subordinates over taxation rights in Ionia. Then there was more Spartan support, when the Peloponnesian League dispatched its fleet, a few hundred soldiers, and reinstated an exiled mercenary commander to aid Cyrus in his attempt to seize the throne by force.

That led to the famous battle of Cunaxa and Xenophon's Anabasis describing the retreat of 10000 Greek mercenaries through hostile territory. It also led to a Spartan invasion of Persia's Greek cities in Anatolia from 399-394 BCE, which only withdrew when the Corinthian War started in Greece and King Artaxerxes II offered massive financial and military aid to the anti-Spartan coalition helmed by Athens, Thebes, Corinth, and Argos. They accepted immediately and it led to a brief but successful joint Perso-Athenian naval raid on the Peloponnese, in which the Satrap of Phrygia, Pharnabazus II, handpicked an Athenian governor to rule the conquered island of Kythera.

Unlike Sparta, Athens supported a Persian invasion and conquest of Greek territory on and near the mainland for the first time since Xerxes' invasion a century earlier. They could hardly blame the Spartans for accepting Persian gold at that point. Direct Persian military intervention mostly ended after that first joint campaign while the Persians refocused their own forces to deal with Cyprus and Egypt. However, the Persians continued to fight Spartan forces in Ionia and provide financial assistance for the anti-Spartan coalition. That led Sparta back to negotiations with the Persian Satraps in the Aegean in 389.

This delegation argued that full anti-Spartan victory would just lead to Athens rebuilding the Delian League. By then, Artaxerxes II was more concerned with Cyprus and Egypt, but Persian resources kept getting drained into Greece, so the King struck a deal.

Persia switched sides. They gave Sparta funds to rebuild their fleet and the Persian fleet in Ionia and the Hellespont would support them militarily. This new alliance became public knowledge when the Persians openly backed the Sparta in a naval standoff near Abydos. By then, there was obviously no shame in accepting Persian aid as both sides had been doing it for decades.

Tiribazus, one of a half-dozen Satraps of Lydia who had come and gone throughout this period, presided over a peace conference at Corinth, where he presented Artaxerxes II's ultimatum: All the Greek cities of Asia would be ruled by Persia, as would Cyprus and a few choice islands. All the other Greek cities in Europe and on the islands of the Mediterranean would be completely independent of one another, with no intervention to force favorable changes in government or exact tribute from cities outside their own home territories. The end result is alternately called the King's Peace or the Peace of Antalcidas.

Thereafter, the King's Peace was the benchmark for Greek negotiations and inter-city treaties for decades, basically up to the Macedonian conquests. During the Boeotian War, all of the major parties sought out Persian mediation, ultimately resulting in Artaxerxes making an exception for Theban hegemony rather than getting pulled back into Greek Wars. During the Athenian Social War, just the threat of Persian intervention was enough to get Athens to release its allies from the Second Athenian League, an alliance whose charter painstakingly assured that it would not violate the King's Peace when it formed to fight Sparta in the Boeotian War.

Over the course of the late 5th and early 4th Centuries, the taboo on Greco-Persian cooperation was effectively broken, even though it remained a rhetorical device to criticize political opponents.