That doesn't mean you can't talk to them, despite their clear indication that they don't want you to.
Of course, not all women are open to being approached. In fact, not a single one of them is open to being approached because that's precisely why people wear headphones in public.
However, if you still believe your wishes to talk to a woman override her desire not to speak to you, here are some pieces of advice on how to attempt to do so as she recoils from you so fast that she redshifts away from you.
As the light of her form increases in wavelength and shifts into the red spectrum as she flees from your presence at a significant fraction of the speed of light, it can feel like an obstacle difficult to surmount. It is even more difficult to surmount than getting her to take off her headphones and talk to a creepy guy (e.g. you) approaching her in public when all she wanted to do was live a life untouched by skeevy PUAs.
It can be attempted, though!
What to Do to Get Her Attention
Stand in front of her (with 1 to 1.5 parsecs between you).
Have a confident, easy-going smile.
If she is still looking at you, simply attempt to get her attention by broadcasting via a radio telescope. Send out signals in her direct line of vision so she can hear it.
The fact she has refused to take off her headphones is a boon in this case. She will be able to hear your signals. They will be distorted by the Doppler effect and will have the effect of making your voice sound deeper, so make it brief, but know that you will sound manly for once.
Broadcast on as many frequencies as possible "I want to talk to you for a minute."
If she gives you the finger, that means you're getting through to her. You should do what we call "Acknowledging the Awkwardness" by giving her a rueful shrug so as to say "guilty as charged." You're halfway home now.
She, on the other hand, will be well on the way past Proxima Centauri by this point.
Try to keep the conversation going. There may start to be some delay at this point due to light speed lag due to the cosmological distances between you, but fear not. You're used to long delays in hearing back from women you've attempted to talk to! This is just like that!
If she refuses to speak to you at all, she may have slipped into the event horizon of a black hole. You've won an important moral victory, regardless.
Try again next time. Definitely don't give up or leave any woman unharrassed. If she's in public, she's fair game. For you and your ilk.