I was really surprised by some of the responses. First of all, the OP sounds like a super-nice person who generally considers others' viewpoints and would like to do what's good for her family, but also knows what really stresses her out. The ILs seem like people who think "my way is the right way" and are unwilling to consider any other viewpoint as valid*. They also have already shown disregard for the couple's boundaries, putting their own selfish desires to see the baby as soon as possible above what may be best for the baby, the mother, or their own son.
Here's the thing. The whole deal about becoming a parent is that it's a huge responsibility but then you also get the commensurate privileges to make these decisions. The only time this is questionable is when there is clear harm to the child, which is not the case here. Therefore, the new *parents* get to decide when and even if, any visitors see the baby. The desires of the grandparents are far below the needs and desires of the parents and the baby. Doesn't matter if it's a question of immunization, potentially contagious disease, or just inconvenience or stress. And THERE IS NOTHING WRONG WITH THIS. It's not immoral, it's certainly not illegal, and it should not be guilt-inducing.
To the OP I would say, start practicing keeping your boundaries in place now, and saying no to violations of them politely, firmly, and repeatedly. This will come in handy not only with the ILs but also once your baby turns into a toddler!
* to the folks who say "well they're old-fashioned". OK, that's fine. But there's a way to be old-fashioned and still allow that other people might do things differently:
"Huh. So, you'll be changing some diapers, son? I never did, because men just didn't do that when you were a baby, and your mom and I were fine with that."
Or, there's a way to be an asshole:
"You're going to be changing diapers, son? Why, that's a job for your little lady! There's no way I would ever change a diaper in back MY day, when MEN were MEN!"