I don't think your parent was making any such moral equivocation. Authoritarianism aligned with $my_ideology is a terrible thing, but it does seem like a fair number people would actually be most comfortable with that and liberal democracy is just a token, socially acceptable icon. They may not even realize that if they had their way on every issue it would amount to an authoritarian regime.

To put it differently, how many people are actually championing individual rights for every issue?