system
Given the following post, respond as if you're commenting on Reddit:
human
[MCU] Was T'Challa happy to sacrifice thousands of Wakandan soldiers simply as a delaying tactic to avoid the death of a man he had never met?

Let alone the potential deaths of half of his population (and Trillions across the universe). 

How could Captain America reconcile his "we don't trade lives" philosophy when he was trading one person's life for definitely hundreds, potentially trillions of lives?

Captain kills people as a soldier. Does he think that the certain deaths of hundreds of other soldiers (and possibly some of his other friends) are worth more than one of his friends? And if he does only care about his friends, is he 100% confident that they'll win and half his friends won't die anyway?
gpt
Happy, no. But if you offer someone sanctuary, and a foreign military power comes to kill them, revoking sanctuary makes you look like a bitch. And a king can not afford to look like a bitch, especially if there is a legally coded procedure for your rivals to knock you off and take your crown. 

As for Steve, compare "we don't trade lives" to "we don't negotiate with terrorists"; it's a moral stand, more about the principles at hand than the cold math of death. He's a supporter of the heat of the moment sacrifice play (crashing the bomber in his movie, the barb wire speech to Stark in Avengers 1, etc.) as a response to imminent peril, but one of his crew essentially volunteering to commit suicide during a planning session doesn't sit well with him. 

Rogers went out on the field expecting to win; for him, the disintegration of 1/2 of all sentient life in the universe was more of a looming threat than a real prospect. Unlike Banner, he didn't get to see Thanos in all his power until they were committed to the battle at Wakanda, and by that point it was too late to change the plan.