Please forgive the Enquirer-esque subject line. Of course, I actually know nothing of the religious beliefs of Dr. Hayek, but I strongly doubt that he was a Baptist of any sort, let alone a Southern Baptist. Not, however, because his philosophy made it impossible. As I’ve hinted before, I know of no religious beliefs as compatible with classical liberalism as Baptist (at least, properly understood).
In recently discussing The Road to Serfdom with Ben, he pointed out a passage I had not previously noticed which illustrates a part of this.

What our generation is in danger of forgetting is not only that morals are of necessity a phenomenon of individual conduct but also that they can exist only in the sphere in which the individual is free to decide for himself and is called upon voluntarily to sacrifice personal advantage to the observance of a moral rule. …Only where we ourselves are responsible for our own interests and are free to sacrifice them has our decision moral value. We are neither entitled to be unselfish at someone else’s expense nor is there any merit in being unselfish if we have no choice.

I suppose that, in order to make clear how this relates to Baptist belief, I’d better explain a little bit about Baptist belief.

There are a few core principles in Baptist theology—so few that theology seems a little strong of a word. The two central tenets are the lordship of Jesus Christ and the authority of the scripture (because of its status as the revealed Word of God). Those are really the only things Baptists have in the way of canonical beliefs.
This is because the primary principle of Baptist theology is the priesthood of the believer—each Christian is responsible for following the guidance of the Holy Spirit in reading scripture, and that responsibility is primarily to God alone. Baptism is designed to be a very tolerant religion, and a very individualistic one. If it doesn’t deal with those two central things, then differences in belief between you and another are really not between the two of you—they’re between each of you and God.
As you might imagine, this lends itself to a very decentralized organization. Each church is responsible for its own organization, including deciding its theology and calling its pastor. Churches then form associations at the local level, and conventions at a larger level, to enable themselves to cooperate voluntarily (thus, the Cooperative Program is one of the ways Baptist churches pool funds) to advance God’s work. (For a better and more complete picture of Baptist beliefs, please read The Baptist Faith and Message, by Herschel Hobbs.)
And as you can hopefully see from this brief sketch, it is a religion ideally suited to being a libertarian. Sadly, it’s not always practiced that way. Just as most people forget to ask whether a thing is something government should do or not, many Baptists have forgotten to ask whether the issue of Adam’s bellybutton (or lack thereof) in any way challenges the lordship of Jesus or the authority of scripture.
This also hopefully sheds some light on the large number of denominations (for those who aren’t Baptist). Many issues are subjects of long-standing debate, and different denominations of Baptists are the result of long-standing positions in those debates. Now, one of the things on which (I have the impression that) most Baptists agree is free will. Free will is the idea that humans freely decide to accept or reject salvation—that God does not make the decision for them. God gives us free will, allowing us to make decisions against His will, because that is the only way our decisions to follow His will have meaning.
And so, I submit to you that Hayek at the very least would have agreed with Baptists on this point. Government cannot make you a better person. It can only make you act like a better person. In so doing, however, it makes you a worse person—just as Mill observed in regard to the truth, morals, like muscles, decay when they are not exercised.
Now, if we can just get more Baptists to agree with Hayek…