Is it okay for a neutral or ground bus bar to extend behind breakers and have connections only accessible by removing breakers?
I do not think so it is also wrong to have two neutral wires under one screw needs to be repaired by an electrician .
The panel has been designed and listed that way. If I were an inspector I don’t think there is anything to say.
That looks like GFCI or AFCI Breakers, they stick out farther than standard breakers. Like Jim said, Square D built it that way, but it is a pain to work around. I am sure when the full AFCI / GFCI breaker rules go into full effect manufacturers will come up with better layouts
The breakers connect directly to the bar. It’s designed that way. It eliminates the need for a separate grounded conductor from the breaker to the bus for afci and gfci breakers. It usually eliminates the curly pigtail conductor. Don’t know why the used thr pigtail style here, because they have far fewer terminals to land them on.
The double tapped grounded conductors are improper.
I think that the panel is designed for the Homeline breakers which plug directly onto the neutral bus without the pigtail conductor. It’s supposed to eliminate the extra conductor from the breaker to the neutral bus on afci and gfci circuits. It looks like they used breakers with pigtails, which left them short on accessible terminals. The double tapping is improper.
If you still can verify that the afci breakers used are listed on the panel label. I suspect that they are but worth checking if possible.
I agree,
Sorry I disagree ignoring double taps is wrong.
Jim, a bunch of us here like to take on the mfg. and anyone else we can to show our vast cognitive abilities…
There are two discussions going on here Roy.
Unless: OP wants the panel re-manufactured so the neutral connections (which are double tapped) can be seen… 
I don’t think that anyone here is advocating leaving the double taps. The neutral terminations behind the breakers is not a issue.
The topic of the thread was about the access to the bar. I stayed on topic and answered the question.
Let it go Jim.
Several Canadians are having a touchy day. Think it’s the change in weather!
I Don’t blame them…