Wikipedia's citation from 1893 says the term comes from sunburns on farmer's necks which would predate any supposed communist symbolism.

"poorer inhabitants of the rural districts ... men who work in the field, as a matter of course, generally have their skin stained red and burnt by the sun, and especially is this true of the back of their necks"

Frederic Gomes Cassidy & Joan Houston Hall, Dictionary of American Regional English VOL.IV (2002) p. 531. ISBN 978-0674008847