At one point, Gargron, the main guy behind Mastodon, even mentioned using a trumpet as the basis of Mastodon's logo branding: https://github.com/mastodon/mastodon/issues/962
"Toot" also has the double entendre. In all my life, I've never heard anyone outside a playground use it to describe flatulence. In my personal experience, it's almost always been about the musical notes. I'm not in a band or otherwise around musicians more than the average person, either.
There's nothing more to it than that: A quirky name based on the chosen logo, following the Twitter example.
I agree it wasn't the best word choice, and I can understand why it has been de-emphasised in favour of 'posts', but the reasoning behind it was logical.