When did guitar led worship music become accepted? When did guitar based worship music become common and accepted in church worship, when organs used to be the standard.
The acoustic (non-electric) guitar is an instrument with a very soft dynamic range relative to most other instruments, such as the organ, or wind instruments, and is not effective in leading large assemblies in worship. The electric guitar was invented in 1931, but the electric signal from the guitar required amplifiers to increase the volume of the sound, s without amplification, the signal from the electric guitar has a low dynamic range, too. Guitars began to be used in church when amplifiers became small enough to be portable, and became inexpensive in the late 1960's. The use of guitars in worship services was also encouraged by the liturgical reform movement that enveloped many denominations in the early 1960's, perhaps partly a consequence of the social consciousness engendered by the folk movement of the late 1950's and 1960's, where such songs as "If I had a hammer", and "We shall overcome" bore witness to a sense of social justice that conformed with Jesus' teaching. The electric guitar came to be used in these settings, in part because by this time it, and the associated amplifiers and speakers were inexpensive, and relatively portable when compared to the organ, and was a close match in volume to an organ for accompanying a group of people.

Most of those building what are today known as mega-churches adopted the guitar, and other non-traditional accompaniment styles, probably in part because they wanted to differentiate themselves from congregations in traditions where the organ was still more or less widely used, because of the inflexibility imposed by the size and immobility of the organ, and I suspect, in part, because of the expense and lead time involved when purchasing an organ.