The phrase "dumb sheep" refers to people who are easily influenced, ignorant, or blindly follow others without thinking for themselves. Full definition
I once read something by some sociology academic that basically said that it only takes 10 % of a population to start perpetrating and promoting a myth on a regular basis before it quickly becomes an «accepted fact» by the general population, and many of the remaining 90 % will happily trawl out the party line like dumb sheep. (justarsenal.com)
It is too bad Muslims are such a flock of dumb sheep incapable of thinking for themselves. (religion.blogs.cnn.com)