I2start: I agree with your questions about vaccine schedules - unfortunately I'm not aware of any studies or supporting lab evidence to show whether there is added risk from bundling vaccines, or administering on a time-compressed schedule. It is something that probably should be studied. Of note though, many of the illnesses that prompt the vaccines also tend to strike on a compressed schedule (e.g. usually before age 7), and that's got a lot to do with how the schedule was designed.
Maddy: Not sure I understand what you're getting yet. Yes, the measles clusters have started with index cases that came from overseas, but we haven't been given any information to suggest that there's a practical way to prevent this. One of the problems with measles is that the disease can be transmitted for days before it's diagnosable. It might be reasonable, though, to add a question to the visa applications about immunizations, and to add measles to the list of required international immunizations (which currently is limited to yellow fever).
There may or may not be a rise in autoimmune diseases - remember that many of them could not be diagnosed until recently which does NOT mean that they didn't exist previously, and there's been a big increase in conditions like fibromyalgia, celiac, chronic Lyme, and chronic fatigue that have become fads and are enormously overdiagnosed. Sadly, there are a lot of physicians only too happy to prey on people who go diagnosis shopping. Your PhD friend might not be aware of these things. But, it is certainly reasonable to expect that "environmental crap" is not good for us. So where do you start? Fluoridated water, preservatives in food, growth hormones and antibiotics given to meat & milk animals, contaminants in water, unnecessary medications, airborne pollutants, outgassing of furniture and home building materials....quite a long list, and most of these have not been studied to nearly the extent that vaccines have been. If anything, I'd consider vaccines to be the safest of these. Despite a ton of studies there has never been any hint of a link with vaccines and autoimmune disease. If that's the basis of the antivaxxer argument (a theoretical worry with zero evidence despite extensive testing) then the bar for anti-science must be at an all-time low.