At an excellent colloquium on Tradition, Culture and Citizenship run by the Tradition Project of St. John’s Law School, a central question was what kind of politics allows traditions to flourish in the modern world. For me the clear answer is classical liberalism.
The classical liberal order leaves space for tradition in two ways. First, it justifies a state which has its object only providing the public goods that the family and the market cannot provide. As a result, the state has no business imposing wide ranging obligations that may burden traditional practices, so long as those practices do not interfere with these relatively few public goods, like the rule of the law, national defense and the regulation of substantial externalities, like pollution, that the state provides.
Second, classical liberalism recognizes that mediating institutions, like churches and mutual aid societies, are themselves important producers of public goods. It is these mediating institutions that are best at handing down traditions from generation to generation.