Is it safe to manually clear out AzureCache and AzureTemp folders?

Hi Refell. According to preventing Azure cache bloating you should use scheduled task Clean Azure storage cache for cleaning local folders

Although not backed by any documentation or proper research ;) I'd always consider anything with temp or cache in it's name to be "outlawed" for sudden disappearance.

Of course there could be some tasks or requests half way through that might get a unexpected hick-up, so if you have a Site that does anything with things like Money, legal, scheduled imports/exports, have 3rd party systems rely on it's response, etc... you might want to be a bit more careful and just use the solution Mikhail mentions.