Everyone feels really different about this stuff. I was actually way more relaxed with the baby than I thought I would be. My DS1 was born December 12th and we had plenty of visitors and had him at mass and all the Christmas functions.
People were asked to wash their hands and of course anyone visibly sick didn't hold him. Most people I would say use common sense and would not put your newborn in jeopardy, but never hesitate to questions someone of course.
The whole whooping cough scare wasn't really around then or for DS2 so I never requested anyone have vaccines before they could see my baby. In fact we have a play group where I found out later some of the kids aren't vaccinated and it was never an issue.
I didn't take DS1 on any child related events until he had his shots at 2 months. With DS2 and this baby I already have toddlers so that is not even a possibility to avoid as I plan on continuing play dates and our schedule classes. I have mentioned getting certain vaccinations to family members as a suggestion but I would never insist they get them.
All my kids are born in the winter months with the flu and everyone has been fine without me being to overly protected or insisting everyone they come into contact with has vaccines.
My kids in general have been pretty healthy and have luckily not contracted anything serious. If you plan on nursing I think it really does help with sickness.
I know some people are more cautious than myself and that is not wrong just different and you will see what your comfort level is when you have your baby.