Ultimately the choice is yours. All I can give you is my perspective.
I am MTF but only part time in appearance so usually when I present as female it is when I'm at nightclubs. In a way that makes things even more dangerous because I usually drink (although I keep it at a responsible level) and am surrounded by drunks as well. Long story short, I never accept rides from a stranger. I only accept a ride from someone I actually know if it is an emergency. That is in part because I own a car myself so I really don't need rides to begin with. I am also extremely choosy as to who I allow in my car.
I don't get in strangers cars mainly due to safety issues and convenience. Once you are in someone else's car, they are in control--not you. They may seem sober at first but after a couple of miles down the street you realize you have a dangerously drunk driver on your hands. Second, since you don't know them you also don't know where they live or where you are going. They may tell you they will take you to such and such place but they are in charge of the steering wheel--not you. As the drive goes on, you could get more suspicious and eventually have to jump out. That could mean a long taxi drive back to wherever you were and hopefully you were smart enough to bring enough money for it. Even then, you have now wasted time and money. As to safety, you don't know who the person is and it is literally the roll of the dice. They could take you to a destination with no questions asked on one hand or on the other hand you could have a knife or gun right to your head the moment you close the passenger door. I'd rather not put myself in those situations.
Additionally, question the motive of the person and also question your behavior. If you are standing around or loitering for a period of time, then the driver may think you are a hooker and try to solicit you. My advice if this is happening is not to loiter (i.e. find something better to do with your time). If on the other hand, you are clearly walking to a destination and minding your own business and a vehicle is circling you or approaching, I would consider that very suspicious on the part of the driver. Normal people have lives to live and things to do. People going about normal commutes would not have time to even notice your presence on a public street. Anyone who is noticing you enough to pull over and ask you if you need a ride clearly is "cruising" or at minimum has nothing going on. Remember the phrase, "An idle mind is the devil's playground." I have a busy life and therefore anyone who has a life so boring that they are trying to find out where a stranger is walking and why is not getting a pleasant reaction from me.
If this is happening frequently, you may want to question the neighborhood you are in or the venues you are at. Again, normal people with normal lives don't have time to be casing strangers. I consider any pedestrians or vehicles who are loitering, circling, or moving slowly with no apparent destination to be highly suspicious. In fact, I occasionally call the police on such people. It is NOT normal.
You mentioned you have a CWP. So do I but one of the first things I learned with self-defense is the most important tool is avoidance. I want to live a peaceful and meaningful existence. Having to call the police on people, detain them, shoot them, or taser them isn't exactly what I consider an enjoyable evening. No matter how skilled you are or what weapons you carry, each time you encounter problematic people, you are increasing your chances of something happening to you. Nobody is invincible and the goal should be enjoying life--not having to deal with scary people.
Sorry for the long rant but I hope this helps.
