Esther Waters is not treated with sympathy for being an unmarried mother. I don't know if I agree with "vilified" (seems too strong), but Esther definitely did not find support for having a son out of wedlock.
Esther's first job is as a kitchen maid at the home of the Barfields. They are a wealthy family of horse breeders. Esther tries to hide her pregnancy from her employers, but is eventually dismissed. Mrs. Barfield said "I couldn't have kept you on, on account of the bad example to the younger servants."
From this point forward Esther is in and out of work, and the common reason for her dismissal from being a servant in other wealthy homes is that she has an illegitimate son. The connotation that Esther brings with her into these homes is that she is a "loose" woman. That simply won't do for respectable and wealthy households.