Then Moses said, “Now show me your glory.” Exodus 33:18 NIV Was Moses being impertinent by requesting that the Lord should display his physical to him.
The context of the request was the restoration of the covenant between God and Israel following the golden calf incident. When God agreed to Moses' plea to continue to go before Israel, Moses sought confirmation from God as a sealing of the terms of the agreement. "Show me your glory." This is not a simple matter of curiosity on the part of Moses. This was a means of confirming the restoration of covenant. God always confirms his covenants. What Moses requested was a revelation of Jehovah himself that went beyond any encounter Moses previously had with God. He wanted to see God without any protective barriers between himself and the unshielded presence of the Almighty. Moses did not simply wish to see another manifestation of God. He wanted to see God in his actual glory, not just a representational form of God. Moses is not requesting to see some anthropomorphic form or some form that accommodates the frailness of the human frame such as the burning bush or the pillar of cloud or of fire. Moses wanted to see God himself and God agreed with certain limitations.
God told Moses that no man could see His face and live, so Moses was permitted to see God's back. In Ex 24:1-11, Moses, along with Aaron and the others, went up and "saw the God of Israel", but from Ex 33 we assume they could not have seen His face. Ex 24:10 mentions the "feet" of God as something they might have seen. When Moses asked God "show me Thy Glory" in Ex 33, presumably Moses wanted to see more of God than he saw in Ex 24, which, from what's mentioned, may have been a vision of at least the feet of God. So if Moses did indeed get at least a partial glimpse of God in Ex 24, God might not have begrudged him for wanting to see more of God. Conjecturing, in Ex 24 when God warned Moses that the others were not to come up the mountain with him, that Moses was to come up alone, God may have had in mind to show Moses the portion of His Glory He showed him in Ex 33, which turned out to be God's back. But when the others came up with Moses, which they weren't supposed to do, God did not inflict any punishment, instead they all got, apparently, a very limited glimpse of His Glory, in this case, at least His feet. It's not clear, from the warning God gave Moses, whether disobedience would result in punishment of any kind, or if so, that then perhaps God changed His mind once they all came up.
Let's see the context.
15Then Moses said to him, “If your Presence does not go with us, do not send us up from here. 16How will anyone know that you are pleased with me and with your people unless you go with us? What else will distinguish me and your people from all the other people on the face of the earth?”
17And the Lord said to Moses, “I will do the very thing you have asked, because I am pleased with you and I know you by name.”
At this point, the Lord was very agreeable and very pleased with Moses. They were like friends. Then Moses made the amazing request:
18Then Moses said, “Now show me your glory.”
There was no hesitance, immediately
19 the Lord said, “I will cause all my goodness to pass in front of you, and I will proclaim my name, the Lord, in your presence. I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
The Lord didn't rebuke Moses for making the request. Instead, he agreed to do.
Was Moses being impertinent by requesting that the Lord should display his physical to him?
No. The Lord treated Moses like a friend.
The LORD would speak to Moses face to face, as one speaks to a friend.