Are ActionFilterAttributes reused across threads? How does that work?

This will depend on the version of ASP.NET MVC but you should never store instance state in an action filter that will be reused between the different methods. Here’s a quote for example from one of the breaking changes in ASP.NET MVC 3:

In previous versions of ASP.NET MVC, action filters are create per
request except in a few cases. This behavior was never a guaranteed
behavior but merely an implementation detail and the contract for
filters was to consider them stateless. In ASP.NET MVC 3, filters are
cached more aggressively. Therefore, any custom action filters which
improperly store instance state might be broken.

This basically means that the same instance of the action filter can be reused for different actions and if you have stored instance state in it it will probably break.

And in terms of code this means that you should absolutely never write an action filter like this:

public class TestAttribute : ActionFilterAttribute
{
    private string _privateValue;

    public override void OnActionExecuting(ActionExecutingContext filterContext)
    {
        _privateValue = ... some calculation
    }

    public override void OnActionExecuted(ActionExecutedContext filterContext)
    {
        // use _privateValue here
    }
}

but you should write it like this:

public class TestAttribute : ActionFilterAttribute
{
    public override void OnActionExecuting(ActionExecutingContext filterContext)
    {
        var privateValue = ... some calculation
        filterContext.HttpContext.Items["__private_value__"] = privateValue;
    }

    public override void OnActionExecuted(ActionExecutedContext filterContext)
    {
        var privateValue = filterContext.HttpContext.Items["__private_value__"];
        // use privateValue safely here
    }
}