We're paying the CDC $6.9 billion dollars to keep us safe from these diseases. Quarantines may seem draconian but they're an obvious necessity, and given the Internet and things like that, they're no longer nearly as isolating.
Given that we're paying them this quantity of money (although it is actually relatively small), we should listen to their opinion. Many of the quarantines implemented during the Ebola outbreak were against the recommendation of the CDC.
Even if we had 100% of people immunized in the USA, you'd still have to protect your newborns from everyone who came in from other countries, isn't immunized and may have brought the disease with them.
85% of children globally are vaccinated. It's pretty much only extremely remote areas of the developing world where the vaccine is not available (from which travel is difficult), people who are medically unable to receive the vaccine and people in the developed world who have chosen not to be vaccinated for inaccurate reasons.
My dad told me a story about how someone caught measles from being in an elevator a week after someone else who already had it.
This is not likely to be true. Measles is a virus, spread through coughs and sneezes. Baring rare viruses that can form a spore-like outer coating, they do not usually survive longer than periods of time measured in minutes outside of the human body or other similar incubating environment. Elevators are not generally conducive environments to the transmission of disease. A week would be an extraordinary time period for this to occur. Far more likely is that some other contact occurred with an asymptomatic infected person, since with measles people can be infectious four days before symptoms are displayed.
If we accept that people who don't vaccinate are killing people via negligence, then we can easily apply that same negligence to the people who enter without vaccinating.
Doesn't matter where you're from, choosing not to vaccinate when you otherwise could is taking action that can lead to people's death. Some people don't have that option, in which case it's hardly negligence.
Amusingly, if you eliminate a disease from a country, vaccinations for it should no longer be even necessary. I'd still get them, though, just in case one got through the cracks.
In the modern world this isn't really an option. There's too much interconnectivity to think of any country as being isolated.