Pretty sure the answer on the global entry is going to be a no - my husband was supposed to take my daughter for hers, and it was cancelled. The state department issues passports and they are part of the shutdown, so I'm guessing it would be a no on actually getting passports, but as far as I know, post offices will still be accepting applications (processing will likely take longer).
Not to get political, but gov. shutdowns are terrible - we have fed employees sit around for weeks, incurring late fees or getting into debt if they live paycheck to paycheck, then we turn around and pay them, so the taxpayers spend money for services that were not being provided. So it hurts fed employees AND wastes money (not saying the employees shouldn't get paid after the fact, just that its dumb to hold them hostage then spend the money anyway on nothing). Opinions about who to blame are a dime a dozen (there is plenty of blame to go around) but the fact that this situation is even a possibility within our system is a serious problem. So sorry to anyone who is going without a paycheck at the moment!
Here's hoping it will end quickly and won't affect your GE appointment!