I agree a comma immediately following a period or full stop does look weird, but it would look worse without!
"Bob, C.J, Greg and Charles all went to the store."
So your way of punctuating was in the end, correct.
Bob, C.J., Greg and Charles all went to the store.
The rule is that a comma mustn't go after an initial, ever.
I did a bit of research to double check and I didn't find anything that contradicted my gut feeling.
However, you could change the order of names thereby avoiding the inaesthetic coupling of the period and comma.
"Bob, Greg, Charles and C.J. all went to the store."
EDIT: I thought it best to rephrase and change the original modal verb, "shouldn't" to "mustn't" to avoid any possible misinterpretation. I hope, I've made myself clearer!