If a method only accesses local variables, it's thread safe. Is that it?
Absolultely not. You can write a program with only a single local variable accessed from a single thread that is nevertheless not threadsafe:
https://stackoverflow.com/a/8883117/88656
Does that apply for static methods as well?
Absolutely not.
One answer, provided by @Cybis, was: "Local variables cannot be shared among threads because each thread gets its own stack."
Absolutely not. The distinguishing characteristic of a local variable is that it is only visible from within the local scope, not that it is allocated on the temporary pool. It is perfectly legal and possible to access the same local variable from two different threads. You can do so by using anonymous methods, lambdas, iterator blocks or async methods.
Is that the case for static methods as well?
Absolutely not.
If a method is passed a reference object, does that break thread safety?
Maybe.
I've done some research, and there is a lot out there about certain cases, but I was hoping to be able to define, by using just a few rules, guidelines to follow to make sure a method is thread safe.
You are going to have to learn to live with disappointment. This is a very difficult subject.
So, I guess my ultimate question is: "Is there a short list of rules that define a thread-safe method?
Nope. As you saw from my example earlier an empty method can be non-thread-safe. You might as well ask "is there a short list of rules that ensures a method is correct". No, there is not. Thread safety is nothing more than an extremely complicated kind of correctness.
Moreover, the fact that you are asking the question indicates your fundamental misunderstanding about thread safety. Thread safety is a global, not a local property of a program. The reason why it is so hard to get right is because you must have a complete knowledge of the threading behaviour of the entire program in order to ensure its safety.
Again, look at my example: every method is trivial. It is the way that the methods interact with each other at a "global" level that makes the program deadlock. You can't look at every method and check it off as "safe" and then expect that the whole program is safe, any more than you can conclude that because your house is made of 100% non-hollow bricks that the house is also non-hollow. The hollowness of a house is a global property of the whole thing, not an aggregate of the properties of its parts.