So, I'm seeing this from the point of view as a Welshman. It's well known that the English and French fought each other for centuries, so how did English and French soldiers not kill each other while fighting side by side in the Crusades? That's not to mention the other countries at ends in the Middle East.
Which of the Crusades do you mean? I think you are referring to the Hundred Years war when you say that they were a long time at war.
The "nation" as a form of political identity did not really exist until the late 1700s–1800s. People identified strongly with their locality or region and with their religion, but not with a "nation."
Political and military organization wasn't national, it was feudal (let's ignore for the moment that the idea of "feudalism" being a thing is contested). This means that militaries were raised by lines of obligation that had little to do with cultural groupings.
There were many crusades, which in particular are you interested in?
(Sorry this is thin, I'm on my phone)