I believe in reading all of the information available, but also keeping in mind that not everyone with Internet access has been trained to read, analyze, and critically think about scientific data/studies. You have to be EXTREMELY critical of any source you take information from on the Internet because literally anyone can publish anything they want, and you have no idea what their credentials truly are (if they have any).
I'm fortunate to have access to thousands and thousands of peer-reviewed journal articles, so generally I base my opinions on scientific matters off of those. My choice to vaccinate my daughter was based off hours and hours of reading peer-reviewed journals, as well as professional advice/guidelines. I can read until my eyes bleed but it still won't replace the formal training that doctors, immunologists, and health professionals receive. I know people get all enraged by the fact that vaccine manufacturers and "Big Pharma" get paid for this stuff, but that's life. It doesn't automatically make people who have spent 10+ years of their life getting degrees untrustworthy. Plus, you know what would make them even MORE money? Pushing medications and treatments to treat a vast array of preventable, deadly diseases.
Ultimately it comes down to this: People who lost their kids by the handful to these diseases would be absolutely horrified to hear that we were tempting them to come back after being controlled (and in some cases completely eradicated) by not understanding how good we actually have it, how lucky we are to have access to these vaccines.
I don't give my daughter the flu vaccine as its efficacy is questionable and she doesn't go to daycare. We delayed the MMR until after she was 15 months as there's some evidence to suggest it may be more effective after 15 months. So I don't just blindly follow guidelines and schedules. But I do put a certain amount of trust in medical professionals (and I discussed both decisions with her doctor), because I believe it's completely necessary. You probably wouldn't trust yourself to fly a plane by reading stuff online, so I'm not sure why people consider themselves qualified to make decisions that affect public health with that information.