Are you saying that in a same sex or alternative couple, there can't be an identifiable mommy and daddy?
In my experience there generally isn't, same sex couples don't feel the need to adopt hetero norms in order to be good parents.
Children with two parents in the home unquestionably fair better, this is pretty settled social science, not the kind of excrement spewed by grifters like, say, Ibram Kendi to make a quick buck.
It is, although you have to look at why that is. A massive factor is that a single parent generally has a lower income than a married couple, which means they live in a worse area, which means they don't get access to the better schools - the issue is one of social and demographic disparity at least as much as it is of an individual's ability to be a good parent. But I don't think that that is really the point of the statement she's railing about, which very specifically references "a married mom and dad".
It's an absurd assertion, made even more ridiculous by the offering that such rhetoric is in any way extreme or unAmerican and she's getting rightly excrement on for it.
It is extreme, because as I've already pointed out the suggestion that a married mom and mom or an unmarried mom and dad somehow create a less safe environment for a child is freaking ludicrous. It's dangerous, because it foments and supports bigotry and prejudice. Sadly I fear that you might be correct that it isn't un-American to do that, but it should be.
