[Forgive the word vomit... I blame my sleep-deprived brain.]

A certain philosophy? Not really, but there are different subcultures within the traveler community, and the members of those subcultures tend to share certain philosophical or ideological leanings--some more coherent than others. Homeless travel is anti-establishment by its very nature, and as conservatism tends to defend the status quo, travelers skew left by default. You get a bunch of poor, left-leaning young people together and the results are predictable.

In short, you run into lots of communist, socialist, or anarchist-leaning types. Lots of people who are very much into social justice slacktivism, and even a few who've been to a protest or two. Anti-capitalism is a common theme, anti-corporatism/colonialism/imperialism/authoritarianism/-everyotherism as well. Anti-consumerism is also rampant, frequently coupled with a dash of smug self-righteousness. It's less visible on this sub, but pop on over to a site like SquatThePlanet and it becomes readily apparent. Or better yet, just get to know some travelers on the road.

Tldr: Punk, but homeless.

As I said in the beginning though, there is no one certain philosophy. What I described above are merely the most common types of groups you'll run into, and so it's as close as we come to a monolithic identity. Many of us--probably most of us--aren't represented by that description. We may have leftish political viewpoints, but that's true of most young people. We may be somewhat anti-establishment, but that's true of most travelers. Most of us are just doing our own thing for our own reasons.

My reasons? Well. Shit happened, I became homeless. Not having anywhere to go I simply hit the road, and I've been on the road ever since.