I don't. The article mentions that there is currently a cultural bias for women to handle child care. For examples: a) "many senior executives had stay-at-home wives", b) "most men in the U.S. earn more than women, she says, moms are more likely to stay home when children are sick since the loss of the father’s income is more likely to be detrimental to the family budget.", and c) "Studies demonstrate that mothers continue to bear the brunt of childcare responsibilities and companies that provide day care support can reduce employee absenteeism by as much as 30 percent."

As such, women are the most affected by these policies.

The question I see is, are these Momazonians advocating for policies that support all genders equally, or are they advocating for policies which only help women? Your comment suggest the answer is "no" or "only accidentally", but nothing in the article supports that.

My reading of the article suggests that they want "backup day care benefit for employees ... providing help for parents", that is, it would apply to all parents, including single fathers and families with two married fathers.

You mentioned gender neutral terms like 'firefighter'. I think there are better examples which show how a group can use a seemingly discriminatory term to support equal rights.

One example is the National Woman's Party. They had an important role in passing the Nineteenth Amendment in 1920, which provided suffrage - women didn't have special voting rights compared to men, but equal voting rights.

They then proposed the Equal Rights Amendment in 1921: "No political, civil, or legal disabilities or inequalities on account of sex or on account of marriage, unless applying equally to both sexes, shall exist within the United States or any territory subject to the jurisdiction thereof."

Again, equality of genders, not preferential treatment. Indeed, this was a sticking point against the ERA. Women had special treatment. Quoting https://en.wikipedia.org/wiki/Equal_Rights_Amendment :

> Their debate reflected the wider tension in the developing feminist movement of the early 20th century between two approaches toward gender equality. One approach emphasized the common humanity of women and men, while the other stressed women's unique experiences and how they were different from men, seeking recognition for specific needs. The opposition to the ERA was led by Mary Anderson and the Women's Bureau beginning in 1923. These feminists argued that legislation including mandated minimum wages, safety regulations, restricted daily and weekly hours, lunch breaks, and maternity provisions would be more beneficial to the majority of women who were forced to work out of economic necessity, not personal fulfillment

The NWP continued to support equality between the genders in the civil rights era of the 1960s.

Thus, just like the "National Woman's Party" didn't seek special treatment for women, I don't think it's correct to look at a term like "Momazonians" and conclude they want special treatment for moms.

As another example, the National Association for the Advancement of Colored People" seeks "to ensure the political, educational, social, and economic equality of rights of all persons and to eliminate race-based discrimination", not the advancement of African-Americans over other races.