There aren't opportunities to go all the time, but there are numerous opportunities. Also, a new cadet can speak with a chaplain at any time during Beast.
The two main times are Wednesday's and the day of the religious services. I'm Jewish so we had services on Friday night, but there were a variety of services. There were Jewish and Muslim services on Fridays and services for the Christian faiths on Sundays. I also know that during our Beast there was support for Buddhists if it was needed, but I don't know how often it was used.
Many new cadets will go to multiple services as it is a nice break from everything (we had many cadets who would come on Friday's for Jewish services and then also go on Sunday for Christian services). Traditionally, the Jewish chaplain's time/services feature a large number of cadets because the rumor is that the "Jews have the best food." While I'm certainly biased, the difference is between the source in my opinion. For the past three years the Rabbi's wife (who is a phenomenal cook) would make all the food that was present at chaplain's time and religious services. So the opportunity for fresh hot homemade food was there. The Rabbi PCS's at the end of the year, and the new Rabbi's wife won't have the opportunity to cook as much, but I'm sure they'll figure out something.
All of that to say, all of the faiths are welcoming and open to new cadets of any religious affiliation. Whether you're religious or not, it truly is a good time to relax and get away from the grind of things. When religious opportunities are made known, you will know because usually there are a multitude of announcements regarding it. And if you don't here anything, then ask and your squad leader should be able to get you all the information.