To stand against the Otsutsuki Branch Family on the moon, Shinji would need the Hyuga Clan's help.
Only the Byakugan chakra of the Hyuga Clan could resist the Giant Tenseigan's chakra drain. Otherwise, even Naruto, the strongest person below the Six Paths after the Fourth Shinobi World War, might have all his chakra drained in a single encounter with the Giant Tenseigan.
Besides...
If the Otsutsuki Branch Family wanted to activate the Tenseigan, they would also need the pure Byakugan of the Hyuga Clan's Main Family. So, as long as Shinji won the Hyuga Clan over, he could block the Branch Family from activating the Tenseigan and leave them with no choice but to take the risk of kidnapping someone by force!
After considering all this, Shinji, dressed in Akatsuki robes, immediately said to Neji, "I bear no ill will toward the Hyuga Clan, and the Otsutsuki Branch Family on the moon threatens us all. We can work together to deal with the Otsutsuki crisis!"
Neji was overjoyed. "Please rest assured. I'll convey your message to the head of the clan right away!"
"Go ahead. I'll contact you again."
Shinji gave him a brief instruction, then turned and left.
Neji immediately brought the message to Hiashi.
After hearing him out, Hiashi hesitated.
Neji cooperating with the Akatsuki Organization was an entirely different matter from the Hyuga Clan cooperating with them.
If the village learned that the Hyuga Clan had secretly colluded with the Akatsuki Organization, it wouldn't let the clan off easily—even if they had only done so to deal with the world-ending crisis threatening the Shinobi World.
So if the Hyuga Clan agreed to cooperate, it would be giving the Akatsuki Organization leverage over them.
But if they refused, and the Otsutsuki Branch Family destroyed the Shinobi World in