The one I read said that outcome based education was about determining what students should learn, then testing whether or not they actually have learned it. Obviously outcomes could be chosen that support progressive indoctrination, the same way they could be chosen to support conservative indoctrination. There's no fundamental reason Outcome-based Education would support a progressive agenda. Maybe they think it's progressive because it's new. If that's the case its pretty short sited to say something is bad because it is new.
Despite what the Texas GOP says Higher Order Thinking Skills and OBE aren't the same. One is a set of skills people can learn, the other is a method of teaching.