Can “thanks in advance” be considered rude?

To remove any chance of seeming presumptuous, you might say:

Thanks in advance for any help you are able to provide.

This acknowledges that their ability to help may be limited (or nonexistent), but it is courteous nonetheless. It is perfectly suitable for business contexts.

(Note that according to the specific situation, you could swap out help with words like assistance, information, thoughts, etc.)

I prefer:

I would be grateful (or very grateful or perhaps even most grateful) for any help you are able to provide.

"Thanks in advance" may be acceptable in an internet forum, but to me it seems too informal for business correspondence, and does run a risk of being interpreted as presumptuous.

I only ever use it when I fully expect that the request will be acted upon, e.g. a refund for a returned item, and I consider it good manners in cases where you are not going to send a followup after the other party has completed their work.

Depends what the request is. There's a difference between, say, a request for information (thanks in advance), or a request to carry out some horrible task (thanks in advance).

This would be horribly presumptous: Hi Jane, sorry I won't be around to do this in person, but could you let John know his contract isn't being renewed? Thanks in advance.

This is ok: Hi, I couldn't find anything on your website about accessibility. Is your building wheelchair accessible? Thanks in advance.