How to ensure thread safety of utility static method?

Since your class does not hold any member variables, your method is stateless (it only uses local variables and the argument) and therefore is thread safe.

The code that calls it might not be thread safe but that's another discussion. For example, Date not being thread safe, if the calling code reads a Date that has been written by another thread, you must use proper synchronization in the Date writing and reading code.

Given the structure of the JVM, local variables, method parameters, and return values are inherently "thread-safe." But instance variables and class variables will only be thread-safe if you design your class appropriately. more here

I see a lot of answers but none really pointing out the reason.

So this can be thought like this, Whenever a thread is created, it is created with its own stack (I guess the size of the stack at the time of creation is ~2MB). So any execution that happens actually happens within the context of this thread stack. Any variable that is created lives in the heap but it's reference lives in the stack with the exceptions being static variables which do not live in the thread stack.

Any function call you make is actually pushed onto the thread stack, be it static or non-static. Since the complete method was pushed onto the stack, any variable creation that takes place lives within the stack (again exceptions being static variables) and only accessible to one thread.

So all the methods are thread safe until they change the state of some static variable.

It is well known that static methods with immutable objects as parameters are thread safe and mutable objects are not.

I would contest this. Arguments passed to a method are stored on a stack, which is a per-thread idiom.

If your parameter is a mutable object such as a Date then you need to ensure other threads are not modifying it at the same time elsewhere. But that's a different matter unrelated to the thread-safety of your method.

The method you posted is thread-safe. It maintains no state and operates only on its arguments.

I would strongly recommend you read Java Concurrency in Practice, or a similar book dedicated to thread safety in Java. It's a complex subject that cannot be addressed appropriately through a few StackOverflow answers.