No, the main argument against him competing as a woman is not fairness. Women's sports were created for those of the female sex, not for those self-identifying as having a male gender. Whether Hubbard is a good or bad weightlifter, he has little in common with the female weightlifters.
I use male pronouns because he is of the male sex. He only claims to have changed his self-identified gender, not his sex.
Suppose a 16yo boy wanted to compete in an age-14 sports league. You might say that this is disallowed because a 16yo would have an unfair advantage. Yes, probably so, but that is not the reason. If it were, then the age-14 league would be pressured to allow 16yo boys who ' poor athletes. After all, there are lots of 16yo boys who have lesser athletic skills than the better boys in the age-14 league. They could compete without ruing the fairness of the competition, but they would ruin the character of the league, and the league needs to be able to draw reasonable boundaries.
Men do not belong in women's sports, and women do not belong in men's sports.
That being said, I have seen women participate in recreational sports that are mostly men, without disrupting too much. I do not necessarily object to that. There may not be enough players for men's and women's teams. But still, the fairness of the competition is not the main consideration.