Yes, they're not supposed to be related, even if you as an out-of-universe movie spectator know their comic backstory. There are two pieces of evidence for that.
The first is the audio commentary of X-Men 2, over the Mystique/Nightcrawler scene below (timestamp 1:14:13 in the movie, and therefore in the commentary):
Alright, this is uh, this is a big moment, 'cause this is another one of those scenes I think where... It's one of the first scenes I kind of took a step back, because being a nerd/geek, I really wanted to see a moment between Mystique and Nightcrawler. And fans of the comics know that in the comics, they're mother and son. So I really wanted to have a scene that would hint at maybe that's where we were going, but not necessarily there yet. And I think it's also a moment that kind of sums up Mystique's point of view, which we have never really heard up until now.
The second one is located in The Art of X-Men: The Last Stand (2006), page 47:
After the cancellation of “Ms. Marvel,” Claremont and Byrne brought the character over to “Uncanny X-Men” as the leader of a new Brotherhood of Evil Mutants. In the course of
the Brotherhood’s battle with the X-Men, Nightcrawler notices the physical similarities between himself and Mystique and wonders aloud whether they are connected. Two decades later it is finally revealed that Mystique is Nightcrawler's mother, a part of X-Men lore that has not been adopted by the movies.
Now arguably Peter Sanderson, who wrote the "X-Men: From Comic To Screen" text above, was not involved in the making of the movie, but it's reasonable to think he talked with the movie's creators. Furthermore, the above is an official Marvel publication, and I doubt Marvel would have accepted to print such a phrasing if they wanted to have room for a potential "Nightcrawler is Mystique's son" part in the movies.