Putting trailer tires on a car should not be done unless absolutely necessary in an emergency situation and if you do have to temporarily use trailer tires and wheels on your car to get you off the road and into town or to a tire shop then yes it's okay to do so.
But if you do use trailer tires on your car temporarily you should get your current tires for your car fixed and replaced for safety.
Drive slower and safely with the trailer tires if you have to but don't drive for long with the trailer tires on your car.
The reason you do not want to keep trailer tires on your car all the time is that trailer tires are different from car and truck tires.
Trailer tires have stiffer sidewalls and higher operating pressures that help reduce trailer sway and hold up to the load much better.
The tread design on the trailer tires are different as well because trailer tires don't require any traction to keep the trailer going down the road.
The trailer tires also hold up to the extra weight being hauled on or in the trailer.
Car tires have softer sidewalls and better traction tread design and provide a more comfortable ride with the car or truck.
So you should not use any trailer tires on a car or truck unless absolutely necessary and only for a short time to get you off the side of the road.
I have had to use my spare trailer tire and wheel before on the back of my truck once when I had a flat tire on the side of the road and my other truck spare was bad.
Luckily the trailer tire and wheel was the same fit for my truck.
However once I got into a town where a tire shop was I immediately had the tire replaced with my truck tire for safety.