Recently I have observed multiple panelboard installations at different facilities in which the studs used to wall mount the panel are not protected. These studs extend well within the panel and conductors route against them which is not appropriate. In most instances I see red rubber caps installed over the studs to guard against this. Is this specifically called out in the NEC or in any UL standard for the construction of panels?

The factory mounting studs are not prohibited by the equipment listing standards.
This is an installation issue, where the qualified installer should know that abrasion protection must be added as needed.