It's important to note that hot or cold is fine, since God said in the passage I would rather that you were hot or cold. Since God does not desire anyone to perish, this would point to the purpose of cold and hot water as a metaphor.
Yes,
both hot and cold are fine because they both represent a distinction from "common" or "the world."
Back when I was a young troop in the military on my first tour overseas to Thailand during the end of the Vietnam War, I got off the plane and was met by my sponsor, an older troop who had been there a while.
He took me for lunch to a little restaurant just off base that catered to the US military personnel. The restaurant was deserted except for us--there wasn't even a server visible. He walked past a buffet table that was filled with sliced meats and bread and sat at a table.
We sat there for a while, waiting for a server. Eventually, I got antsy and suggested just getting some food from the buffet.
He said, "Ohhh, nooo! You don't want to do that! You don't know how long that food has been sitting out there. It might have been there since Monday!"
Then he leaned close to me and said, "Look. In these Third World countries, if they take the food right off the fire, you can eat it. If they take the food right off the ice, you can eat it. But if it's room temperature, spit it out! It will kill you!"
Even in Jesus' time, it was known that food kept hot stayed edible, and food kept cool (such as in a gourd in a flowing stream) stayed edible. But food allowed to stand lukewarm would quickly spoil and become toxic.
It is being different from the world--"
a peculiar people" that Jesus is talking about. It's what the Lord has always been talking about--He hasn't changed His message.