You should really cheer for the Packers! Not much bad-blood between the two teams/fans, yet. Fellow NFC North member.
CHI and MIN fans cheering against us I get (I cheer against those two all the time), but Green Bay & Detroit don't seem to have that beef....right now atleast. It's likely coming in the next few years though.
As far as the Packers fans who live in Wisconsin and Lions fans who live in Michigan and Northwest Ohio, there really isn't much hatred there.
But we all know those people who are Packers fans just because they like John Deere or Brett Favre or whatever. As it happens, one of my least favorite people who was a roommate of mine is a Packers fan. Last year during the Super Bowl, I was conflicted. I HATE the Steelers and their fans so I was kind of ok with Green Bay winning, but I did not want my acquaintance to have the undeserved feeling of accomplishment that comes with winning the Super Bowl.