Oathkeepers association is irrelevant
Of course they would deny the allegations. It doesn't really matter whether they do or not. As it stands, this isn't anything out of the ordinary, unfortunately. The fact that there are organizations like DCYF shows this is not the first time a child has been taken away. You'd think they'd wait until a judgement had been entered against the parents before they actually take the children away, but I'm sure there are all kinds of policies and ways they can take "emergency action" to immediately take children without a judgment.
The only issue I can possibly see here is that the association with the Oathkeepers was used to expedite the process of taking the children away, or to do so without the proper procedures being followed. And if that does turn out to be the case, there have almost certainly been other cases where flimsy allegations were used to illegally speed the process up. The solution would seem to be that the authorities need to stop these shenanigans, if that indeed is the case. If the association with Oathkeepers was used as a lever, it's a bit worrying that they could use it, but I'm sure it wouldn't hold up for long, and if the authorities are using that sort of thing to expedite the process, there's nothing stopping them from using pretty much anything they want, or even false allegations. They might as well have listed "picking toes in Poughkeepsie" as a reason.
While that's not a good thing, the courts so far seem to shoot most of those things down, and it's on par with the other garbage so-called "authorities" pull in violating our rights. Hasn't come to a new level quite yet.
Hopefully the Oathkeepers angle will get all this ironed out so they follow all the proper procedures in the future, if they didn't do so in this case. Maybe the Oathkeepers were the wrong "interesting tidbit" to spice up the case with.
The couple will have to convince the courts that they are indeed fit to retain custody of the children in spite of the allegations of abuse and risk to the children which have been leveled against them. I'm sure the Oathkeepers angle won't get more than a minute in court.