It isn't necessary to read music to play the guitar, but it can be helpful. Many of the great guitar players can't read music, but play entirely by ear and by their intimate knowledge of their instrument.
Everyone, however, names the notes and chords and these relate to the traditional dots of the page of written music. From the word go, when a beginner starts out learning to play the guitar, they learn chord shapes and name them and learn the relationship between chords. This could be called music theory, but it's an integral part of becoming a musician and developing your musical ear and playing an instrument.
So no-one should be deterred from learning to play the guitar because they can't read music, nor should they hesitate for the fear of having to learn to do it.
The use of tab (tablature) in the guitar world offers an alternative to reading music, and a useful one, in that tab states where notes are to be played, on which string. Tab is very useful but has its limitations, and shouldn't be overused to the detriment of developing your technique, knowledge of the instrument and your musical ear.
The great news is that listening to music plays a major role in developing your musical ear and understanding. I find this with adult learners who have been music fans all their lives - this provides a solid base to draw on as they learn to play the acoustic guitar and develop their style.