Yes. And no.
When I was 18, I looked older. I always had to go buy the beer. I once took a date to a bar type of place and they checked her ID, she was old enough, but didn't check me and I was not. They figured that a beautiful woman would not be with a much younger kid. A stripper in a bar that I went to and tried to pick up spotted my real age immediately and informed me that she didn't date younger men. She probably thought that I just wanted to get laid. She would have been right.
But mostly, this never came up while dating. Very few wanted to go on a second or third date but it wasn't age related. Another story for another time. Some of the womens fathers had a bit of an issue but I think that mostly they were worried about me screwing their daughters.
Now that I am older. Much older. I think that I look a bit younger than my age. Especially if I keep my hat on. Not a bad thing. I had to prove my age a couple of years ago to get the senior price on a haircut and discount coffee. Women still avoid me like I have the plague, so it probably isn't age now either.
I honestly don't know why this is a problem or comes up. If she is shallow enough to not go out with you because she thinks you are too young, she probably will find something else wrong anyway. It is just a convenient excuse. Next time show your ID and see what happens.