Not sure how this is "US Authoritarianism" but okay...
In any case, two things could be at play: either the family is truly conservative and thought white conservatives will accept them; or they are playing the respectability politics. If it is the former, many say most immigrants would be conservative voters (because many are religious and entrepreneurial), if it weren't for conservative politicians and base demoraphics in their new country being racists. If it's the latter, we all know those who present themselves as "one of the good ones" are grifting and acting in self-preservation. I have a mate who posts far-right stuff online and supports Trump, even though he himself is a brown immigrant (I suspect his father--who isn't exactly the sharpest tool in the shed-- may be influencing him as well).
Those who play respectability politics are acting in self-preservation. This is actually a tale as old as time. As one user here pointed out, there was a Jewish organisation who are Nazi supporters. During World War 2, Jewish elders and organisations in Europe actually gave names of their members to the Nazis. They thought they could save themselves or more lives if they cooperated. Hannah Arendt covered this tidbit of history in her book on the trial of Adolf Eichmann, from which the famous term "banality of evil" came from. Of course, the book caused controversy not just because it posits that evil people feel casual of their actions, but also that it brought the taboo that several Jewish leaders in Europe have enabled the facilitation of the Holocaust.
For the record, I am not trying to be anti-Semitic with my post, I'm only explaining the result of playing respectability politics in the case of anti-Semitism and Holocaust.
I think the fact that there are so many bigots out there being disproportionately vocal and often working to recruit others to their way of thinking with couched language and dogwhistles make it too easy for some people to assume that anyone speaking negatively of an oppressed group is a bigot.
The trick is usually identifying whether the negativity is about "all" of a group, or just some of them, but subtlety can be challenging in a text only format at times, especially if stuff ever gets taken out of context.
There's a lot of corruption in my government, at national, state and municipal levels. Not every citizen is corrupt (many are, how else would you survive without being shunned/blackballed? Unless you already gained stability some miraculous way --lotto, large inheritance?) and your post boils down to something I've been pondering for a few months: those who disapprove corruption without calling out benefit from corruption. It's the madam/working girl, bully/bullied mentality. At least in my area, I don't think it's fear of life and limb, since most people I see are willing to risk life and limb on corruption, but I guess there's a difference between going out relatively quickly rather than being tortured to death.
I hadn't thought of it that way before! I guess that some folks either try to work with the system but succumbed to it before they realise it; or they gave up entirely and join.
A favor here, blind eye there. Then people have something compromising on you, so you do another favor and another,; there are mouths to feed. I've said it before, selling our souls is seldom done in one dramatic moment, but rather incrementally.