This has never happened to me as of yet, and I hope it never does. What a horrible thing to have happen.
I would probably do my best to calm the person down and tell them that they are paying me for my expertise. I would try to convince them to please let me talk first and listen carefully to what I am saying, then they can contribute and we can have a civilized discussion about the reading. But they must at least listen to what I am saying and be willing to consider alternate possibilities to what they think they may know. Tell them that everyone has a different viewpoint and that you two came together for them to get a message from the Universe, delivered through you. I would try to stay as calm and collect as possible, since that might help them calm down too. If you can tell in advance that they're uptight or that there might be problems if certain "threatening-looking" cards might come up, I would try having an alternate deck with you, such as the Fountain Tarot, that might not elicit such extreme reactions from clients.
If the client was freaking out and out of control, I would ask them to do the things above, but if that tact did not work on them, then I would tell them they had several options - to calm down and continue on, to end the reading and try again at a different time (maybe try via telephone so they won't see the cards), or to end the reading and part ways as amicably as possible. Sometimes people are just wackadoodle and there's nothing you can do. You need to have confidence in your own abilities (I am not saying you don't) in the face of anyone hostile to your readings (whether it be an extreme religious person or a person like this). You need to have good boundaries and lay down your rules in advance if possible.
Maybe you can make up a written agreement/waiver that the client signs. I would specify that once the reading starts, they agree to pay you for the reading (this should be enough incentive to keep them listening and not get too out of hand). I would also specify that you reserve the right to end the reading at any time for any reason and that they will pay you commensurately for your time and effort. For instance if you had to go to their house and the reading was supposed to go on for an hour and you just laid down the cards, I would make them pay for travel time, gas, etc. That may be going too far, but I myself would stipulate it.
Just think of this as a learning experience. Next time you will be more prepared if something like this should happen. Maintain your boundaries and your "zen"-like (calm and collected) attitude as much as possible. Don't feed into the craziness, just try to maintain your calm inner core and trust in yourself that this is not about you or your ability to do a great reading, this is THEIR stuff. My trick is that I pretend to be the Dalai Lama. I say to myself without inputting any of my personal emotions or biases, and as objectively as possible: "Look at this person and their out of control emotions. Poor thing, I wonder how they got so fear-based. What can I contribute to this person as compassionately as possible so that they will benefit from it." If I would be in the middle of the reading, I might ask the person what they think is going on in the reading and why, as well as what is their personal contribution to things playing out that way and what can they do to change it. Also, would they consider xyz as an alternate way to see the cards. I think this might help empower the sitter and help bring the person into the reading as a co-creator of the reading. If they're still hostile and reactive, I would end the reading. There's only so much you can try or do.
This might be a bunch of mumbo-jumbo, but I hope it helped. Probably others will have more valuable contributions. I myself am interested in hearing what other people say. Good luck to you!