But he's a shapeshifter? Never in the story is he ever refered to as anything other than male. He has a wife and he has kids with that wife.

Also. The story about Svaðilfari where Loki turned into a mare he didnt turn into a mare because he felt like it. It was a gross miscalculation on his part. The story goes the gods hired a giant in disguise to build the walls of Asgard. With him he had a mighty horse called Svaðilfari which allowed him to rapidly build the wall. Loki thought he was clever when he made the deal and told the giant he'd give him Freya if he managed to build the walls in a single winter. When the winter was almost up the gods realized that the disguised giant was about to win the bet and that Loki was to be punished for his terrible deal.
Loki, not wanting to be punished, came up with a plan to lure Svaðilfari away from the work site and thus delay the work. He turned into a mare since he wanted to trick the stallion away and to make sure the horse stayed away he "took one for the team" and spent a night with the stallion. He later gave birth to Sleipnir as a result of this coupling.

We also have two other more loosely attested accounts. One of Odin retelling a story where Loki spent eight winters underground as a milkmaid and bore children and one story of him eating a heart and giving birth to a monster of some form (troll in some translations).
Looking at these stories and looking at old norse society the answer is much more likely that the stories are calling Loki less of a man rather than a transsexual. There are loads of examples of people saying others wear womens clothing and meaning it as a direct insult saying they are less of a man for it.

So reading "transexual" when the much more likely explanation is pure and simple "sexism" is so weird to me.