There is no inherent antinomy between "conservative" and "liberal". Talking iun thiose terms is a bit like talking as if the opposite extreme to North was West, or the opposite extreme to "black" was "green".

If you want an opposite for "conservative" you'd have to use some word such as "progressivist" (I avoided "progressive" there because it sneaks in a value loaded implication). Similarly the opposite of "liberal" would be "repressive", or simpler still, "illiberal".

There's no reason on earth why the most change resisting conservative in the world shouldn't also be extremely liberal in their opinions, more especially of course if they lived in a society which was liberal to start with, so that opposing change meant opposing illiberal ideas.

Good place to live, that would be.