Yeah. It's got to be a parody. Just reading through it, it's far too self aware, and seems to be almost mocking the stereotype of the racist Trump supporter in places.
Which makes it no less vile and hateful. It just reads like the work of someone who thinks they're much cleverer than anyone reading it. Pure troll. If I wanted to track down the culprit I wouldn't be looking at parents - I'd be looking at older siblings or, unfortunately, people with no personal connection to the nursery.
And I wouldn't use the term "false flag" either - not in the traditional sense. Would be way too easy to write something that's more convincing as the work of a racist parent. This is written to be read, and to show the 'superior intelligence' of the writer.