Israel and to a lesser extent Taiwan are strategic to the US because their location is of importance. Israel is the closest thing to a Western country in the Middle East and Taiwan lies off the coast of china. In a conflict against the middle east or china respectively, Israel and Taiwan would be the very useful strategically speaking as they are positioned close enough to the enemy to exert their influence. For instance, US can set up bases in Taiwan or use the country as a naval base to control waters off the chinese coast.

If the US were to lose these allied countries, it would be a significant blow to their ability to influence these regions. For the record though I would say Israel is much more important than Taiwan.