The short answer is yes!
Glass shower doors are completely safe for use, as are most glass shower doors if produced, and installed properly! Showers are typically Tempered Safety Glass which is 5 times stronger than annealed (regular) glass and the safest option for your shower door. Tempering manufacturers in the US have to meet or exceed standards so that you can feel at ease with your safety around the glass. You won’t need to worry about anything after your door is installed; just sit back and enjoy the beauty of your new doors!