It's a long and fascinating story that involves China firing missiles to affect the outcome of Taiwan's first democratic election, as well as the largest American military action in Asia since the Vietnam War.

In summary, the KMT upholds a "One-China Policy", which makes them a natural ally of the CCP against any Taiwan independence movements.

https://en.wikipedia.org/wiki/Third_Taiwan_Strait_Crisis

Back in the day, the KMT (Nationalist party) was the conservative counterpart to the progressive CCP (Communist party).

After the civil war stalemate, this left the mainland with only a progressive party and Taiwan with only a conservative party.

Then Taiwan developed its own progressive party. And nowadays the CCP is becoming much more conservative under Xi... so... yeah...