An alternative to "Old Wives' Tales" to avoid implying old women are likely to be wrong

Solution 1:

The term shibboleth is used with this meaning.

Merriam-Webster defines this sense:

shibboleth

1a: a word or saying used by adherents of a party, sect, or belief and usually regarded by others as empty of real meaning

• the old shibboleths come rolling off their lips [Joseph Epstein]

and Dictionary.com:

shibboleth ...

(3) a common saying or belief with little current meaning or truth.

Solution 2:

myth

Any place you see the idiom "old wives' tale" used, you can insert "myth" into its place.

urban legend

If you're instead looking for another idiom for "old wives' tale," you can readily insert the idiom "urban legend" into its place. While "urban legend" tends to denote newness instead of oldness, what is considered new and what is considered old is relative and is highly subjective.

Solution 3:

Folklore

From the American Heritage Dictionary definition

a. A body of widely accepted but usually spurious notions about a place, group, or institution: Rumors of their antics became part of the folklore of Hollywood.
b. A popular but unfounded belief.

You may have to rephrase to make it work in place of “old wives’ tale”, but it keeps the sense of oral traditions.