Reasonably objective, yes. Otherwise, it just ends up being "this game is dumb and I think it sucks". A good reviewer should be aware of their own bias and should attempt to mitigate that somewhat. Of course, at the same time, it's impossible to be completely objective and no one should strive to throw away all of their feelings about what constitutes an enjoyable experience.
The best reviews will offer a bit of each side.
As an example of completely subjective, look at comments on forums like VGC. This being a Nintendo heavy forum, if I asked for people to give their opinions on the latest FPS game on XO/PS4, you can bet a lot of responses would be some variation of, "lol fps game are boring I don't like this game lol." Does anyone want professional reviewers to be like that?
The best reviews I've read have a reasonable amount of objectivity.
