We have had jersey sponsors in rugby league in AUS for about 40 years.
We have accepted it as the clubs have needed the income to remain financially viable. This is where we are probably different from the NHL in that sponsor revenue from jerseys would be relatively small compared to all of the other revenue.
Our retail jerseys are the same as the on-field jerseys except for kids jerseys where clubs are sponsored by alcohol or gambling companies.
Most fans are fine with it as long as the sponsor logo/artwork doesn't contrast too greatly with the overall jersey design. We have a chest sponsor, sleeve sponsors, "neck" sponsor and top rear and bottom rear sponsor. We also have 2-3 shorts sponsors and the same sponsors on their training gear etc.
This obviously seems like a lot compared to the current NHL standard of none, but they can be blended in quite well, and as it was fairly gradual it didn't cause too much of a problem for fans.
Some clubs have different sponsors for their home versus their away strips.
My club, the Canberra Raiders, have jerseys as follows: