Part of the problem is that Trek uses the Prime Directive to describe two related but effectively different protocols.
Non-contamination only applies to pre-warp cultures. They're not supposed to be contacted or influenced until they're considered "ready".
For warp cultures, it's non-interference...the Federation and Starfleet aren't supposed to impose their will or beliefs on other cultures, particularly by force. Of course, there are limits to this. Warp cultures are out there, a part of the greater interstellar community. The Federation interacts openly with them, which can involve diplomacy, trade, and even war.
Federation members are expected to conform to certain Federation standards, but nobody's making them join.