This is a meme that has been making its way around pop culture for a while now which I fully disagree with.
You should have a basic respect for all people, but definitely not all their opinions. The only opinions that matter are ones based in facts and evidence.
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The definition of respect varies greatly. I respect people's opinions in that I will listen to them, hear them out, and try to see where they are coming from. This does not mean i will agree with or even acknowledge their opinion if it is stupid/horrid enough.