Be careful, consider for a moment what do you want.
If you fancy her then trying to "chat her up" with some "chat up line" will fail, for the average young lady it will get on her nerves and scare her off. If you fancy a woman then you are better off talking to her about the weather than you are using a chat up line.
If you just want friendship and company then if you have a shared interest then you should talk about it, if you do not know if you have a shared interest then you could ask her if she has seen or heard anything of interest recenty and then talk with her about it.
I would advise you to stay away from contraversal subjects, at least until you know the other person well. Regardless of what you think about a issue it does not mean that the other person shares your point of view on the topic. Also even if you share the same point of view you may come across as a freak if you bring up some contraversal subject, even hardened activists who campaign on a subject need to take a break from the subject every now and then.
While men do want to associate with women for romance, it is perfectly possible (and normal) for men and women to be just friends.
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Health is a state of physical, mental and social wellbeing and not merely the absence of disease or infirmity

I am not a jigsaw, I am a free man !
Diagnosed under the DSM5 rules with autism spectrum disorder, under DSM4 psychologist said would have been AS (299.80) but I suspect that I am somewhere between 299.80 and 299.00 (Autism) under DSM4.