I do not know if you are talking bout politically conservative, republican/conservative political parties or what, but:
lib·er·al/ˈlib(ə

rəl/
Adjective: Open to new behavior or opinions and willing to discard traditional values.
Therefore, somebldy that discarded traditional values (slavery) and changed the traditional behaviour is by definition liberal.
con·serv·a·tive/kənˈsərvətiv/
Adjective: Holding to traditional attitudes and values and cautious about change or innovation, typically in politics or religion.
WHile somebdy that tried to keep hold of old traditional ways of life (slavery) would be conservative.
Therefore somebody that changed the traditional ways cannot, by definition, be conservative. Sou can not be for the radical changing of society and be a conservative, because that is the very opposite of the definition of conservative.