I happily hauled a friends horse along when I got my first trailer and we went trail riding. Before I got my own trailer I was hauled to shows by other kind folks but it was people I had a good relationship with.
They knew I had a need and offered.
Just because you have a trailer some who don’t will ask for a lift. I would never haul for someone I didn’t know well and especially for a horse that I had no way of knowing how they take to being trailered.