Canonical is a company full of geeks and hackers, most of us are very security and privacy conscious, and most of us use Ubuntu every day ourselves. We do our best to provide a good balance between privacy and usability

Whether or not Ubuntu is "safe" is going to depend on your own threshold for that term. Clearly the majority of mobile device users feel Android and iOS are "safe" enough to use, and by that standard I think Ubuntu would easily quality as safe as well.