These definitions are from Merriam-Webster:

Conservativism

a political philosophy based on tradition and social stability, stressing established institutions, and preferring gradual development to abrupt change; specifically : such a philosophy calling for lower taxes, limited government regulation of business and investing, a strong national defense, and individual financial responsibility for personal needs  (as retirement income or health-care coverage)

Liberalism

a political philosophy based on belief in progress, the essential goodness of the human race, and the autonomy of the individual and standing for the protection of political and civil liberties; specifically : such a philosophy that considers government as a crucial instrument for amelioration of social inequities (as those involving race, gender, or class)

Liberal and conservative are ideologies. Republican and Democrat are party names. Party names do not change, but the ideology of those parties can shift over time. Ronald Reagan started as a Democrat, then, when the party’s ideology became more liberal he became a Republican. Likewise there have been Republicans who made a party switch to Democrat when the ideology of their party no longer fit with their belief. Currently the Republican party leans heavily conservative, and the Democratic party leans liberal. This hasnot always been the case.

Again. if you look up the definitions of “Liberal” and “Conservative” you will not find the words “Democrat” or “Republican”. That is because the party names DO NOT define the ideology.

Southern Democrats heavily resisted the Civil Rights Act. It represented achange in their tradition that they did not agree with. In doing that theywere behaving in a definitively conservative manner.

There was no Republican party until 1854, Lincoln was elected in 1860 with a heavily abolitionist platform, which caused the immediate secession ofseveral Democrat leaning southern states. Why? Because the abolition ofslavery represented a change in their lifestyles and traditions. That, by definition, is a conservative stance.