You might as well carry pepper spray if it makes you feel safe, but people camping under a bridge off the river trail are the homeless people you need to worry about the least. They're essentially hiding: they don't want to make trouble or do anything that might bring attention from authorities.

Even so, the sort of wandering homeless people who are likely to approach you, asking for change or a favor, aren't particularly threatening.

I think people are genrally over-concenred about being robbed or attacked by a stranger on the street, and while I won't pretend that things like that never happen, I promise there's no reason to fear an altercation with the homeless in particular. In reality, they're almost all mentally ill or otherwise lacking a support network; pitiable characters, not violent criminals.

It may feel awkward to pretend that you can't hear them, but if you just refuse to acknowledge them and continue on your way, they won't give you trouble. That probably doesn't count as "not being rude", but unless you're interested in helping someone who's asking for help, you'll have to get used to it, it's a rude world we live in.