which instrument, invented by the greeks, was the first to be widely accepted for use in christian worship?

The organ

Explanation:

It's one of the ancient musical instruments in History. Invented by the Greek engineering Ctesibius in the 3rd century BC, the organ was introduced in the Roman Empire on the 1st century AD, and after the rise of Christianity became part of the musical instrumentalization of the churches. Its strong tone and atmospherical effect combined with the Gothic cathedrals that became common in Europe in the 13th century.