Why did Elrond let Isildur take the One Ring?

Because he didn't want to fight with an ally and didn't expected it to go this way, as explained in middle-earth.xenite.org:

Q: Why Did Elrond Let Isildur Take the One Ring?

ANSWER: In The Lord of the Rings Elrond tells the people at his council how Isildur took the One Ring for himself:

`I was the herald of Gil-galad and marched with his host. I was at the Battle of Dagorlad before the Black Gate of Mordor, where we had the mastery: for the Spear of Gil-galad and the Sword of Elendil, Aiglos and Narsil, none could withstand. I beheld the last combat on the slopes of Orodruin, where Gil-galad died, and Elendil fell, and Narsil broke beneath him; but Sauron himself was overthrown, and Isildur cut the Ring from his hand with the hilt-shard of his father’s sword, and took it for his own.’

At this the stranger, Boromir, broke in. 'So that is what became of the Ring!' he cried. `If ever such a tale was told in the South, it has long been forgotten. I have heard of the Great Ring of him that we do not name; but we believed that it perished from the world in the ruin of his first realm. Isildur took it! That is tidings indeed.’

'Alas! yes,' said Elrond. `Isildur took it, as should not have been. It should have been cast then into Orodruin’s fire nigh at hand where it was made. But few marked what Isildur did. He alone stood by his father in that last mortal contest; and by Gil-galad only Círdan stood, and I. But Isildur would not listen to our counsel.

”This I will have as weregild for my father, and my brother,” he said; and therefore whether we would or no, he took it to treasure it. But soon he was betrayed by it to his death; and so it is named in the North Isildur’s Bane. Yet death maybe was better than what else might have befallen him.

I think from this passage it’s pretty clear that Elrond didn’t simply “allow” Isildur to take the Ring. Elrond would have had to fight with Isildur to force him to destroy the Ring, but it seems the Ring was capable of influencing the people around it even from the time of Sauron’s death. We can argue and debate about what Elrond’s options were but there is no truly satisfactory answer.

Elrond and Cirdan may have refrained from taking action against Isildur simply because it would have been unthinkable to them. They might have viewed his decision as rash and expressing poor judgment but they were still his friends and allies.