I personally never read for someone who does not believe in Tarot or who is not willing to at least suspend their disbelief enough to take it seriously. To me I find it a waste of time. As people can only believe what they are willing to believe. If you believe that Tarot does not or cannot work, then you will look for proof that it doesn't work, and if you look hard enough you can find something that will convince you of anything.
The media portrays Tarot on a rather negative light traditionally. There is no one really I think who has never actually heard of Tarot. So those who no nothing about it really is probably have heard some unduly negative things about it, and misleading ones.
Reactions can range from fear (or even terror), through distrust of the reader ...
If you are talking about someone with no prior experience of Tarot suddenly receiving a reading they did not ask for, that imho is morally wrong. The person might feel angry that someone looked into their private affairs without persmisson for one thing, and it is not right to confront someone with info they may not be emotionally ready to handle. If they did not request the reading, you don;t know if they are emotionally ready to receive what comes. And even them sometimes what comes is a surprise fo the querent.
The idea, in and of itself, that Tarot works can really be scary to a lot of people. It challenges their view of reality. And when what you have believed all your life to be the true nature of the universe suddenly turns out to be untrue that can be really scary. Thus the expressiion that a reading was "scary accurate".
Tarot challenges our views on reality. It tells us in most cases that reality is other than we were brought up to believe it is. The future is changeable and it can be predicted to start with, to mention 2. And that there is a force that sends us answers to questions when we ask to name another. Someone has to be ready to take these things into consideration that they may be real before it's right to read for them. You can't just confront someone with something they may not be ready for emotionally, like changing their world view.
Babs