(Speaking as an unqualified outsider) Both Poly1305 and Salsa20 are creations of Daniel Bernstein / djb, who seems about as highly respected as you can be in the crypto community. And NaCl, the library they use that implements them (also by djb), is often highly recommended as a 'good' crypto library to use.
That said, it does go against the usual advice not to trust code from people who make their own encryption rather than using existing standards, but maybe this is the exception?
There was an article recently with some good commentary about how uneasy some people feel with how much of modern crypto being used in production is coming from relatively few people, including djb, but I can't seem to find it now...
Older column by Aaron Swartz on djb: http://www.aaronsw.com/weblog/djb
Relevant tptacek comment: https://news.ycombinator.com/item?id=705165 (no idea if this is still valid)