When did the practice of Shinto and Buddhism become separate in Japan?

From what I can see they were practiced as one for quite a long time.

Shinto has evolved from traditional Japanese shamanism and was well established by the time Buddhism made it on to the island. After then one began to influence the other.

When the Meiji emperor came to power in 1868 he declared a policy of sundering the connection between Shint? and Buddhism (this split is called ShintosSiunri in Japanese). This put an end to syncretism between Shint? and Buddhism, although many of the new religions that have appeared in Japan since the early 1800s, while ostensibly basing themselves on either Buddhism or Shint?, have in fact mixed elements of the two in a new synthesis.

Budhism assimilate with local faith such as Thao, Hindu, Konhucu, Christianity, and Shinto itself

Shinto never had a name until the 6Th-7th centuries when the Chinese religions began to be imported to Japan. At that time the term "Shinto" was coined to distinguish the native religion from the foreign religions. The foreign religions, particularly Buddhism, became popular with the court so the Shinto priests did a very clever thing: They made Shinto the guardian of Buddhism. This resulted in a Shinto shrine being beside every Buddhist temple. It also allowed Shinto the focus on ritual elements for harmony in this life rather than on what happens after wards which was taken care of by Buddhism. Because they were in the same complexes, they influenced each other to a high degree and I doubt that most people really separated the two--even though the priests remained mostly separate.

This state of affairs lasted until the Meiji Restoration of 1867 when the government forcibly separated the two so that Shinto could be used to help modernize Japan and promote nationalism. This lasted until WWII when the militarists were removed from power. However, Shinto and Buddhism still retain separate facilities and most Japanese belong to both. You'll also see Buddhist elements in Shinto shrines and vice verse because the guardian Shinto Kami were renamed to Buddhist deities or the Buddhist deities were renamed to Shinto Kami depending on whether the religious cent re went to Shinto or Buddhism during the Meiji Restoration.