Why did Turkey suddenly okay Sweden and Finland joining NATO? It was a case of the necessary prevailing over the ideal

 The American Enterprise Institute's Elizabeth Braw, writing at Defense One, explains that it was a matter of waiting out some internal dynamics in the Scandanavian countries:

What happened? In their trilateral June 28 memorandum—which NATO Secretary-General Jens Stoltenberg and the Biden administration had no small part in bringing about—the three countries agree that “as prospective NATO Allies, Finland and Sweden extend their full support to Turkiye against threats to its national security. To that effect, Finland and Sweden will not provide support to YPG/PYD [Syrian Kurdish People's Protection Units and the associated Democratic Union Party], and the organisation described as FETO in Turkiye.” It went on: “Finland and Sweden unambiguously condemn all terrorist organisations perpetrating attacks against Turkiye, and express their deepest solidarity with Turkiye and the families of the victims.”

There was one particular Swedish legislator who was driving a lot of the support for the Kurdish groups:

This was a victory for Turkey. Last November, Sweden’s governing Social Democrats had promised to deepen their cooperation with PYD, a left-wing Syrian Kurdish party that is also an affiliate of Turkey’s PKK. Why would the Social Democrats promise to deepen their cooperation with this unlikely partner? Because they were trying to find a parliamentary majority for their minority government, and to reach the already-precarious position of a one-vote parliamentary majority, they had to assuage Amineh Kakabaveh, a member of parliament who had been sacked from the Left Party and was sitting as an independent. And Kakabaveh, a former Peshmerga fighter, made maximum use of the leverage by demanding support for Kurdish causes. In fact, she seemed to take delight in her sudden power.

But time was not on Kakabaveh's  side:

But in late June, the Swedish parliament completed its term; it will resume after the country’s parliamentary elections in September. Prime Minister Magdalena Andersson no longer owed anything to Kakabaveh, who can’t be reelected, and could sign the memorandum with Turkey. So, of course, could Finland, which was never really a concern of Turkey’s in the first place.

The bargain finally struck certainly has a lot of benefits for Turkey:

Although the devil of every intergovernmental agreement is in the implementation, the Swedish-Finnish-Turkish memorandum was a certainly a victory for Turkey. In addition to denouncing support for the PYD, Sweden and Finland promised to lift their suspension of arms exports to Turkey and to “address Turkey's pending deportation or extradition requests of terror suspects expeditiously and thoroughly, taking into account information, evidence and intelligence provided by Turkey.” 

What that means was explained by President Recep Tayyip Erdogan in Turkish media: Sweden will have to extradite 73 suspected terrorists to Turkey, he announced. Washington, meanwhile, signaled that it’s willing to sell Ankara new F-16 fighter jets and modernization kits for its existing F-16s.

Mutual security comes with costs:

. . . as a senior official in a NATO member state told me, “Sweden and Finland have learned their first lesson in collective defense”: some members of the collective may be difficult, obnoxious even, but for the benefit of enhanced security for all you have to work with them. 

History provides many examples of nation-states having to hold their noses to pursue bigger-picture objectives. This is one of them. At a time of gruesome behavior and alarming rhetoric on the part of Russia, the West needs to provide the most united front it can muster.