Anti-Vaccination Movement - At What Point...

It would become religion when checkable facts are replaced with pseudo-logical beliefs that one would share without checking their veracity or ever trying to question it. Which, coincidentally, is pretty much most of your pictures among the Anti-Vax gallery.

Hypothetically never.

The scientific method exists to try and eliminate bias and faith from experiments.

If it stops relying on repeat experiments and relies more on claims of individuals. it stops being science.