As being in the “shidduch parsha” and having this discussion i guess i will put my two cents in (in a males perspective).
First, if your parents are the paying for the dates and you plan on having them support you after you get married, then they have every right in whom you should date. If you don’t want them to tell you who you date, my advice is not to expect any support from them and go out, get a job, and live your own life. That is what i have done.
Second, i came across the following quote which is apropos: “Your parents, they give you your life, but then they try to give you their life.” Again, if you want to live your own life, get out from their shadow and GO. Keep in touch with them, even live in there house, just gain some independence.
As noted in the previous posts, if you are mature enough to get married (and hopefully you are since that is why you are dating) then you should be mature enough to go out without having your parents holding your hand the entire courtship.