This can be very challenging to hear, and I think there are a good many Christians who aren't really sure how to respond. And the main reason why is because they're not really sure what the term means.
To claim that someone has "blind faith" is to suggest that there is absolutely no evidence for the things that person holds as true. In other words, they are telling you there is nothing that backs up your beliefs in any way.
All I can say is "Wow!!"
Let me be clear. For anyone to make that claim about Christians proves only one thing: THEY KNOW ZERO ABOUT YOUR CHRISTIAN FAITH.
I can't emphasize this enough. There may be some belief systems in this world that truly require blind faith, but Christianity isn't one of them!
So, if someone said that to me, my first reply would be: "The term blind faith suggests you think there are things which I believe that have no supporting evidence. Of which of my beliefs do you speak?"
Then, of course, you need to be ready for their response. It could include doubts about the Bible, or the existence of God, or some other topic that troubles them...and you need to be prepared to give them an answer for the reason for your hope. (See 1 Peter 3:15) But let me just say that you should never consider yourself at a deficit in this discussion. Christianity has the most incredible evidence known to man! But the followers of Jesus need to know what that evidence is and they need to also know how to defend it.
Here is a link to a series I did in the summer of 2016 to help you out.