As long as they are similarly endorsed by a recognized standards organization, they are a safe alternative. Wear solid shoes with heels. Never ride barefoot, in sandals, or in slip-on shoes such as loafers. Your feet must support you in the stirrups, and flimsy shoes can fall off or get in the way. Heels are important to prevent your foot from going all the way through the stirrup and getting stuck.
Sneakers are unacceptable.
A lightweight, ankle-high boot with laces is ideal. Wear comfortable but not overly baggy clothing. Tight jeans do not stretch and are uncomfortable to ride in. Very loose clothes can chafe, or catch on fences or tree branches. Sweat pants or exercise tights are a good choice.