[T]he divine law orders man for this purpose, that he may be entirely subject to God. But, just as man is subject to God as far as will is concerned, through loving, so is he subject to God as far as intellect is concerned, through believing; not, of course, by believing anything that is false, for no falsity can be proposed to man by God Who is truth. Consequently, he who believes something false does not believe in God [SCG III, 118, 3].And more:
 Besides, whoever is in error regarding something that is of the essence of a thing does not know that thing. Thus, if someone understood irrational animal with the notion that it is a man, he would not know man. Now, it would be a different matter if he erred concerning one of man’s accidents. However, in the case of composite beings, the person who is in error concerning one of their essential principles does know the thing, in a relative way, though he does not know it in an unqualified sense. For instance, he who thinks that man is an irrational animal knows him according to his genus. But this cannot happen in reference to simple beings; instead, any error at all completely excludes knowledge of the being. Now, God is most simple. So, whoever is in error concerning God does not know God, just as the man who thinks that God is a body does not know God at all, but grasps something else in place of God. However, the way in which a thing is known determines the way in which it is loved and desired. Therefore, he who is in error about God can neither love God nor desire Him as an end. So, since the divine law intends this result, that man love and desire God, man must be bound by divine law to bold a right faith concerning God.Now this is not to say that one's knowledge of God must be perfect in the sense of lacking nothing. Abraham and Moses and David knew God, but they did not know him as fully as Christians may do so today. We are finite, after all.
 Moreover, false opinion holds the same place in regard to objects of the intellect that vice opposed to virtue has in regard to moral matters, “for truth is the good of the intellect.” But it is the function of divine law to prohibit vices. Therefore, it also pertains to it to exclude false opinions about God and matters concerned with God.
It's pretty likely that part of what St. Thomas means here depends a lot upon technical definitions of knowledge and opinion. That which is known is that which is certain and could not be otherwise, while opinion has to do with that which could be otherwise. So I might suppose, for example, that I "know" my birthday falls on a given date, but in fact I don't know it (in the sense that Aquinas probably means in SCG above) at all. It's not possible for an infant to know his birthday, so he must be told. But those who tell him may be mistaken, or they may forget, or they may even lie. So really I have an opinion about my birthday, not knowledge.
Now there are things that we may know about God by way of reason - as St. Thomas attempts to demonstrate in SCG especially. And we may know still more by way of faith, which is even more certain. But it's not so that every Tom, Dick, and Harry Average must be a theologian on the order of an Aquinas or St. Augustine in order it to be said of him that he knows God. It seems to me that this means that we must acknowledge a distinction between what the Catholic knows formally, by virtue of being Catholic, and what he knows materially. He intends to know and believe those things that the Church teaches, so that formally it may be said that he knows God; but he then has the obligation, as he has ability and opportunity, to know God materially - to make this knowledge something subjectively true.