I included attached graphic as part of a recent PowerPoint presentation, to scuttle any ideas of a short-haired, beardless Jesus. As your posting implies, the "Church of God" sect claims that traditional images of Jesus are a Roman Catholic invention. If anyone invented this traditional image it was Eastern Orthodoxy, with its attachment to the mandylion, whatever that was.
I obtained the graphic merely by googling "Jewish Rabbis Images", obtaining several pages of them, and merely did a Print Screen on this one.
Most of these Jewish Rabbis have long hair and beards, unless they’re liberal, bald or female.
The bald ones wear skull caps. The ones with high hats, I’m given to understand have their hair tied up inside the crown of their hats. Ian Wilson makes some such comment about this.
It is unlikely that Rabbi Yeshua was clean-shaven with short hair. That was more the style of the Greeks that Paul was addressing, when he evidently preferred his converts to conform to reasonable fashion and not be unnecessarily provocative by defying reasonable cultural norms.