Like others, i try to always finish the back of a piece. To me, it is not "finished" with the raw wood on the back. That is clearly just my opinion and preference and plenty others do not see an issue with it.
My niece bought a large round wooden sign with her newborn's name, first and middle, and date of birth on it. She changed the name of the child after she ordered the sign (they had agreed on one name before she was born, then they decided on a different one after she was born ). So, then she wanted to know if we could change the name on it. I agreed to do it and cut the name out on the scroll saw. When I got the round board to remove the original name done by the Etsy seller, I was appalled to find the back was not finished in anyway, it was simply unfinished wood on the back. Given what they charge for these signs - I couldn't believe they hadn't put any finish on the back side. Yes, it hangs against the wall and nobody sees the back - Until it is taken down. But to me it made the piece look cheap and not done. I personally would never buy a piece that did not have the back finished in some way with at least the stain or seal coat done. However, with this sign, I don't know you would have known until it arrived since she bought it off Etsy. I never checked the listing.