Seems to me more like plain conservative response. Libertarian position would be to protect individual liberty against both state and societal oppression. E.g. In 'On Liberty' J.S.Mill discussed mainly societal oppression (by social norms) as it is more prevasive and insidious than state oppression.
"Sister for sale! One sister for sale! One crying and spying young sister for sale!"
Sub-cultures with anti-natalist norms will find themselves subsumed by those that produce a lot of children. Simple math tells us that the typical American circa 2100 is a lot more likely to be descended from Utah Mormons than Bay Area rationalists.
Descended from today's Utah Mormons than today's Bay Area rationalists. That doesn't mean they won't move to the Bay Area and become rationalists themselves.
> I think their problem is that a private company is doing this, not the Government.
Is that a Democratic take? I think it's a liberaltarian take on it. Here's the conservative libertarian response: raising children is one of the primary functions of society, and social norms that govern private actors make a certain amount of deference to that. Replacing those norms and kicking everything up to the government is a very statist solution, inviting the government into large swaths of human activity where it wasn't present before.