Deuteronomy 32:27 alludes to Exodus 32:
7 Then the Lord said to Moses, “Go down, because your people, whom you brought up out of Egypt, have become corrupt. 8They have been quick to turn away from what I commanded them and have made themselves an idol cast in the shape of a calf. They have bowed down to it and sacrificed to it and have said, ‘These are your gods, Israel, who brought you up out of Egypt.’
The Israelites rebelled and worship other gods. The Lord wanted to destroy them all.
9 “I have seen these people,” the Lord said to Moses, “and they are a stiff-necked people. 10Now leave me alone so that my anger may burn against them and that I may destroy them. Then I will make you into a great nation.”
Moses reasoned with God from the human (anthropomorphic) perspective.
11 But Moses sought the favor of the Lord his God. “Lord,” he said, “why should your anger burn against your people, whom you brought out of Egypt with great power and a mighty hand? 12Why should the Egyptians say, ‘It was with evil intent that he brought them out, to kill them in the mountains and to wipe them off the face of the earth’?
If you kill them all, what would the Egyptians say about you?
14Then the Lord relented and did not bring on his people the disaster he had threatened.
No fear or dread is mentioned in the above account.
Deuteronomy 32:27 Why would God fear these new gods?
The Deuteronomy account presents a summary of the detailed account in Exodus 32. God didn't fear these new gods. It was an example of anthropomorphism, i.e., treating God as if he were a mere man.
26 I said I would scatter them
and erase their name from human memory,
27but I dreaded the taunt of the enemy,
The dread or fear here is related to man, not God. Treating God as if he were a man, he dreaded what the enemy would say about him. This is an anthropomorphic description of God so that we humans could understand the logic of why God didn't destroy the Israelites.
In reality, God had never feared the Egyptians.
The LORD Almighty is the one you are to regard as holy, he is the one you are to fear, he is the one you are to dread.
God fears no one. On the contrary, everyone is to fear God.