Many times have I heard that anti-vaccine people are dangerous even to the vaccinated population. Is that true? If so, how can it be? People say that germs will attack them, and soon they would eventually grow and spread even toward general population which actually got its vaccines.

I mean it's so counter-intuitive: if I'm vaccinated even when disease will spread I shouldn't be in danger.

Biology is rarely black or white, all or nothing. Protective immunity is generally not an on/off switch, where from the moment you're vaccinated you're infinitely resistant for the rest of your life. You shouldn't expect that, having received a smallpox vaccine, you could have billions of smallpox viruses squirted directly into your lungs and shrug it off without noticing. 

Given that (fairly obvious) fact, you should immediately think of scenarios where vaccinated people are still at risk of disease following exposure to unvaccinated people. What about older people who were vaccinated 20 years ago, 50 years ago? What about people whose immune systems are slightly weakened through lack of sleep or obesity or stress? Any of these vaccinated people might well be protected against a brief encounter, but not against, say, being in an airplane seat for 18 hours beside an infected child shedding huge amounts of virus, or caring for their sick child. 

It's all sliders, not switches. You can have a slight loss of immunity (4 hours sleep last night) and be protected against everything except a large exposure (your baby got infected and won't rest unless you hold him for 8 hours). You can have a moderate loss of immunity (you were vaccinated twenty years ago) and be protected against most exposures, but you're sitting next to someone on the subway for an hour. You may have a significant loss of immunity (you're a frail 80-year-old) and still be protected against a moderate exposure, but your grandchild is visiting for a week.
