That's not what due process means at all. It means there must be a pre-defined process for determining guilt or innocence where the accussed has the right to confront his/her accussers and present her/his side of the case. It says nothing about what may or may not be criminalised. Basically it says that justice cannot be arbitrary.
I actually think they used the "priveleges and immunites" portion of the 14 amendment to apply the 4th amendment to the states. I don't know as that is a proper reading of the 4th amendment though, since the 4th only protects "privacy" against unreasonable searches and siezures", not in general.
Now if they will just use the same 14th amendment provision to apply the second amendment, which is pretty absolute, to the state governments. But I won't be holding my breath waiting for them to do so.
I was wrong, they used the due process clauss and a rather strange notion of "liberty" and rights. Scalia ripped 'em bad, but since he was in the minority, it doesn't count for anything.