[I]f feminism simply means supporting equal rights and equal opportunities for women, I don’t see how a feminist can be opposed to government programs that provide poor working mothers with quality child care.
"Equal rights and equal opportunities" are in fact rather conservative concepts when viewed through the inequality of class and other relations.
"Equal rights" in this context is a political concept: it refers to one's relation to the state. To have equal rights means that the government will give all citizens equal consideration in the administration of their affairs.
A good example of this is the present fight over marriage. One side argues for equal rights, the other side against. The gay community advances a conservative position by appealing to the Constitution, their opponents push a "moral" argument by appealing to the Bible.
Similarly, "equal rights for women" means that the government gives women the same consideration it gives men: it acknowledges their right to vote, it defends their right to own property, it lets them seek restitution through the courts, etc. The state treats them equally as citizens, and affords them rights as citizens.
"Equal opportunity," on the other hand, refers to economic relations: it is the right to be considered without prejudice for a job, for example. In theory, a principle of equality of opportunity could be read expansively to mean equal access to resources; in practice, it is read narrowly as "non-discrimination" in the workplace -- a reflection of organized social power around employer preferences.
Equality of opportunity means equality vis-a-vis a particular standard of opportunity. It could be no opportunity, but as long such lack of opportunity is fairly maintained, equality of opportunity has been fulfilled.
This gets at the difficulty of using "equal rights and equal opportunities" as measure of progress within class societies: by definition, some classes have more rights and opportunities than others.
In fact, many rights only become meaningful in conjunction with a particular class position. Rich people can put rights like freedom of speech and due process to work in ways that poor people can't; men might be "most qualified" for a job insofar as they won't become pregnant; the right to vote for African-Americans hasn't translated into an unemployment rate less than 50% greater than the nation as a whole. By itself, an equality of rights doesn't tell us anything about outcomes -- what something actually means for people -- which is one of reasons why it is insufficient as a principle for addressing people's needs.
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When it comes to government programs, for lack of anything else, what Gail Collins says is true enough. We need something that will address these problems, as opposed to nothing.
However, it is perfectly possible to be opposed to government programs in principle and feminist if you endorse something else -- e.g., something that is more likely to address women's concerns than a government program. It might be something designed and implemented by women, for example. "Government programs" typically aren't.
Suffice it to say that in the meantime something has to be extended to people in need -- and it deserves to be developed to a point beyond what a state agency can likely sustain: the point at which people achieve meaningful control over their lives. This is the outcome we should be working toward.