Composing without music theory is like mixing a song without EQ. It’s possible, but I wouldn’t recommend it. Here’s why music theory matters.
The main problem with ignoring theory is that, chances are, you’ve grown up surrounded by Western music. And your ears probably prefer Western music. So the music you inherently prefer will follow the rules of Western music. And by “rules of Western music,” I mean music theory. To break the rules, you have to realize you unconsciously follow them.
It’s been said on this site before that you can’t polish a turd. My own personal iteration of this is “grimy gold is worth more than shiny shit.” The best mixing techniques and experience won’t fix a mediocre composition. Music theory, on the other hand, can.
A tip on “studying” the concepts I’ll discuss: use them. Write songs for the sole purpose of exploring diatonic chords, or do whatever you need to do to make things stick. Just use theory in any way you can and push into territory you’re uncomfortable with as often as you can.
TL;DR: STFU and learn music theory.