can I say, "
I know many people who suppose that health plays a significant role in our everyday lives. But there are others who don't really care about it."?

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The way you said "I know many people who..." sounds like you know them personally. That's fine if you want to say that.

If you want to, you can say
"I know many people suppose..." or
"I know there are many people who suppose..."
meaning that you are aware of there being many people in the world, some you might know personally, some you don't, who suppose that health plays a significant role...