How neutral is "then think again"?

Think again is just an established "set phrase" meaning You are mistaken. I will tell you what you should be thinking.

It's not always an "arrogant" usage. Nobody would be annoyed by an advert saying something like Thought you couldn't afford a Rolls-Royce? Think again!

But it's typically used in contexts like If you think you can pull the wool over my eyes then you can think again - for example, a teacher or similar "talking down" to his charges. It reminds me of You've got another think coming!, which I'd say is always somewhat contemptuous.

I'd certainly advise non-native Anglophones to avoid it unless they're absolutely certain their target audience won't resent having whatever they currently think casually dismissed like that.

If you think "think again" is safe for work, think again.

In AmE, "think again" is a form of finger-wagging or confrontation when it's used directly person-to-person rather than in contexts like the Rolls Royce example FumbleFingers gave, where you'd be happy to learn you'd been wrong. I can afford one after all!

I can think of very few situations at work where that phrase would go over well, especially in situations where you really want to use it!

If you think I'm going to work this weekend because you've been dragging your feet hiring a replacement for Bob, think again.

If you think my direct reports are going to be happy with a 1% raise when I've given them "consistently exceeds expectations" on their quarterly reviews, think again.

I don't think it's used as follows, merely to say that someone is wrong about a fact:

If you think Messi scored two goals in that game, think again.

but I would agree with FumbleFingers that it's about what the other person should be thinking, in the sense that the phrase is typically used to confront someone about their attitude and behavior.

I've been asked to say whether I think the expression is sometimes "arrogant". I suppose it could be arrogant sometimes. But I know that it is probably imprudent to use this expression at work, when it is used in the confrontation mode rather than the you-will-be-happy-to-learn-you-are-wrong mode. And that is the case whether it is used with a superior or with a coworker on your own "level" or with a subordinate.