Is it safe to introduce an unvaccinated pup to dogs that have been vaccinated?

I would say a cautious yes, as my vet told me. As long as you're certain of the health status of the other dog, and the introduction is at the pup's home, all should be well. Ask your vet if you are in any way unsure.
:)

I'm going to err on the side of caution and not risk it. My ex asked if he could take him to see his parents (who have two dogs) when he visits them with our kids.

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Of course we need to exercise caution but don't you run the risk of missing the best age to socialise pups with other dogs if you don't introduce them to any other dog at all? Personally, I made sure I introduced mine to my responsible dog owner friend/keeper of several healthy vaccinated dogs but of course wouldn't consider taking a pup to anywhere I wasn't sure of. I wouldn't put my pup down outside in a public area but cannot see the harm letting them down on a neighbours lawn or in a friends house.

What's the point of having a healthy dog who hasn't been exposed to risk when they have lost their confidence when meeting other dogs as they have spent too long isolated? A few weeks is a long time in a pups life.

I wouldn't be present, have no idea who else is likely to there with their dogs - hence my reticence.

If your unsure of how these dogs will react towards the pup and your not there to supervise, then don't do it, Is your ex responsible enough to protect the pup if anything does happen, think i would be inclined not to if i wasn't there too :)

I'd say go for it as long as the dogs you're introducing are vaccinated. I recently carried my 8 week old cocker pup around while I walked his older half sister. If you err too far on the side of caution then I'd have to exclude the other dog in my house, which is the same as introducing new pups to friends dogs who you know are vaccinated.

Yes he is responsible enough. I have never met his parents dogs and only know of their temperament from what he has told me, neither of the dogs have been in contact with pups before though so I don't know how they would react to our boisterous Labrador. I do want to socialise him as much as possible but obviously balanced with caution.