No, but it makes everything faster: theory is the shortcut for learning, writing and communicating music, not a requirement for playing it.
You can play music without theory, and famous musicians have. But theory is a shortcut: it turns "memorize 200 songs" into "recognize 10 patterns that build those 200 songs".
If you only strum for fun, you need very little. If you want to write songs, improvise, or play with other people, a small amount of theory saves a large amount of time.
The honest answer is that theory is optional the way maps are optional: you can wander anywhere without one, but you will repeat a lot of dead ends. Players who "know no theory" usually know plenty; they learned the patterns by ear and just lack the names.
The highest-value pieces for a practical musician are small: which chords live in a key, how the common progressions sound, what intervals are, and how meter works. That covers most real situations in popular music.
The common fear that theory kills creativity has it backwards for most learners: knowing why something works lets you break it on purpose instead of by accident.
The Beatles-had-no-theory argument deserves its full context: they had extraordinary ears and thousands of performing hours, which is theory acquired empirically. The names are a compression format for exactly that experience; learning them is buying hours.
Where theory matters most: communicating in ensembles and sessions, transposing on demand, arranging for other instruments, and analyzing why a passage you love works so you can reuse the mechanism.
Where it matters least: raw expressiveness, tone, groove and taste, none of which live on paper. The balanced position is ear-first theory: train recognition, then attach the vocabulary, which is the design premise of this site.