I've been playing for over 50 years and thought I was pretty good at rhythm just doing some picking with my friends. We manage to make it through plenty of songs by JD, CSN&Y, Jim Croce, Simon & Garfunkel, Dan Fogelberg, etc.
And I'm a fairly decent strummer and finger picker so when I started playing in our Praise Band about 5 or 6 years ago I was quite surprised to find that I was all over the map when it came to timing and playing with others. At first it was just me on the guitar and a 75-year old fantastic piano player and she set the timing that I had to follow because a grand piano is sooooo stinkin' loud -
Fast forward 5 years and we have a lot of instruments, no grand piano, and click tracks. I have gotten far, far better at timing and counting when I play and that's the big difference for me.
Playing all the chords has never been an issue but now I can't slow down or speed up whenever I want. I have to stay with the beat or it gets really muddy sounding.
So my advice would be to play along on YouTube with the worship songs you like and see how well you do. Pick some songs by Chris Tomlin, Matt Maher, Matt Redman, Kristian Stanfill, etc., turn the sound up, and enjoy.
David