I speak from rubber banding experience here. I've been barrel racing for several years and I have always used thin, figure 8 rubber bands to hold my feet in. And referring to mildot's post earlier,In general, using rubber bands is a safety net to us barrel racers, it keeps our feet in and helps us maintain balance for us as well as or horses because a lot of things can go wrong when you lose a stirrup, most of the time bad.
But also, I must point out that it is also a personal preference. It can either make you feel safe or unsafe, but it is only my choice to use rubber bands at my own risk. It's no use to go preaching to others about what you think, sometimes you just need to figure things out for yourself.