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.
By "Guitar led worship", I think you mean to say a worship band that uses acoustic guitar, electric guitar, bass guitar, drum-set and keyboard, commonly known as Contemporary worship music.
This kind of worship style is very recent and growing, though still facing oppositions from many traditional churches. It's more popular among Charismatic churches. One such example is Bethel Church, where Jesus Culture ministry was formed. If you listen to their music style, it's quite heavy and more like a rock song.
A guitar led worship is a new trend these days and it's hard to know where or when it all began. Since guitar is deeply related to rock music, looking at the history of Christian rock tells us that it started after the 1960s. First there were Christian Rock bands who sang gospel songs using rock music or contemporary styles. They made albums, performed live concerts and made music videos. Leading the worship with rock music instruments was still very foreign to them.
From the 1980s, we started seeing worship bands using modern music instruments. One such example would be Hillsong from Australia. Latter we have Passion Conferences making tours all around the world, making this worship style more and more popular.
There are many examples to mention but I'm just writing them down off the top of my head.
Over the last 20 years the Contemporary Worship movement has steadily grown pushing the organ out of church and replacing it with instruments that are actually relevant to modern culture. The trend has accelerated over the last few years to the point that guitar led worship is close to dominant. Use of the organ is collapsing at 1% a year. http://sowhatfaith.com/2014/09/15/how-worship-is-evolving/
Within the Catholic Church, it appears that this has arisen from 1) a misunderstanding of actuosa participatio populi (the idea of congregational participation), - which it is said was in the first place ill-defined by the Vatican II Council fathers - and 2) from the actions of the innovators.
Therefore answering when within the Catholic Church, it seems these have been ever on the increase after the Second Vatican Council.
Please note that 'accepted' is taken here to mean 'condoned' as such the music is most likely not suitable sacred music for use within the liturgy. Please see the links below.