In this passage philosopher John Locke is making the political statement that slavery is unjust and it is sickening to see his countrymen justify it. It can be assumed that John Locke agreed with what principle of the United States democracy system?

Yes he was one of the enlighten thinkers that the founding fathers followed and created our governments ideals around his ideals for instance he said "life, liberty, and property" and the founding father adapted that but said "presute of happiness" instead, due to the whole slavery thing