Gina Radke posted a picture of herself in a 1970s mink coat on Instagram last year with the hashtag #nonewfur.

“I don’t buy new furs,” said Ms. Radke, 41, of North Little Rock, Ark. “I don’t want to contribute to that market.” The hashtag allows socially conscious shoppers like Ms. Radke to support anti-fur activism by grandfathering in old furs. Or in Ms. Radke’s case, grandmothering them in.

She...