You could use the tenses either way, with a little modification. I'd argue that the bigger issue is the combination of the two parts of the second sentence in each example.
The "trust is very important" phrase doesn't fit grammatically with the beginning of the sentence. By splitting it off and adjusting a few things, you could write those two sentences like this:
Every person that I meet is unique, and I treasure all of them. Trust is very important.
Every person that I've met is unique. I treasure them all. Trust is very important.
The sentence about trust doesn't seem to fit with the rest of the writing, unless you have some earlier context. I'm not sure how you're using these sentences, but you might want to consider moving the line about trust to another paragraph.