If allowing a disabled person to use their products / services would be unsafe, can a business refuse them?

I know that in some cases a business can obviously do that (and are probably mandated to do that), like refusing people with dwarfism to go on certain carnival rides, or refusing to hire people with bad vision to be pilots, but I don't understand how and when are those exceptions allowed.

Edit: I got this question because of another thread on reddit. Here's the situation:

A woman was a common client of a casino. She used a service dog to warn her about upcoming seizures. As she visited the casino often, the employees knew about her condition and her dog. One day she came without the dog, as the dog was ill, and was refused entry / asked to leave. Half of the comments were calling this an ADA violation. The other half were saying that, considering the circumstances, the casino would have been held liable if they have let her in and she had a seizure inside and died, as they knew about the risk (considering that losing in a casino is a potentially highly stressful situation which can induce seizure, and without her service dog there was no way to be pre-warned about it and prevent it from happening) and allowed it, so the casino was mandated to not let her in. Who is right?