[In the first scene, Starling runs obstacle course, alone. She climbs a cargo net.]
The beginning of the film shows Clarice in a stereotypically masculine setting: running an obstacle course, dripping with sweat. Also, she's the only person doing it. She's by herself, not with a group. As a woman, she needs to work harder to get noticed by the FBI.
[As Starling walks through the FBI academy, the vast majority of the trainees are men. At one point, she's the sole woman in an elevator full of men.]
Men men men, manly men everywhere. Men are cleaning guns and otherwise dominating the screen as Clarice walks the halls. She's definitely an outsider because of her gender.
CHILTON: You know, we get a lot of detectives here, but I must say I can't ever remember one as attractive. […] Will you be in Baltimore overnight? Because this can be quite a fun town if you have the right guide.
Clarice is also subjected to sexist comments like this one from Dr. Chilton. He would rather flirt with her than respect her. She knows better than to let a sleazeball like him "guide" her through Baltimore. He's barely one step subtler than Miggs.
CLARICE: I graduated from UVA, doctor, it's not a charm school.
This is the perfect comeback to shoot down Dr. Chilton's remarks about her gender. But because she's a woman, she has to remind him of her credentials to get his mind off other things.
CRAWFORD: This type of sex crime has certain aspects I'd just as soon discuss in private. You know what I mean?
Starling isn't aware at this moment that Crawford is doing this to appease the local police force. He's appealing to their gender bias and sucking up to them in a way by leaving Clarice out of the discussion. They would feel threatened if she were put on the same level as the rest of them.
CLARICE: Excuse me! Excuse me, gentlemen! You officers and gentlemen, listen here now. Uh, there's things we need to do for her. I know that y'all brought her this far and that her folks would thank you if they could for your kindness and your sensitivity. And now please, go on now and lets us take care of her. Go on now. Thank you.
After being left standing in a room full of men who disregard her and lack respect for her, Clarice feels the need to stand up for herself. The men do leave, but they hesitate. Would they hesitate if given the same order by a male superior officer?
PILCHER: What do you do when you're not detecting, Agent Starling? […] You ever go out for cheeseburgers and beer? The amusing house wine?
CLARICE: Are you hitting on me, doctor?
It doesn't stop. Dr. Pilcher, at the museum, hits on Clarice in a similar way as Dr. Chilton. But at least Pilcher acknowledges Clarice's credentials. It seems like he respects her, and that might make her more attractive to him.
LECTER: Billy is not a real transsexual. But he thinks he is. He tries to be. He's tried to be a lot of things, I expect.
Dr. Lecter analyzes Buffalo Bill's gender in a scene that some trans activists object to. What do you think Buffalo Bill's gender identity really is? Is it up to us to decide?
[Clarice finds Frederika Bimmel's Polaroids hidden in her music box.]
Even though the FBI has combed the victim's room many times, these pictures remain hidden until Clarice finds them. How does Clarice find them? Maybe because she's a woman, and she knows where other women might hide things.