Approaching a master's in humanities after STEM-focused undergrad I graduated this past year from an Ivy League university with a double major in a STEM field and Asian studies (with a focus in literature). Throughout university I felt the desire to eventually pursue a graduate degree in the humanities, but for various reasons ended up focusing much more on my STEM work. In my final year, I took some courses in religious studies that reignited my long-held interest in that field. Since graduating, I've been constantly reading books and papers on religion while working in tech. I think I'd like to pursue a master's in religious studies, both as a way to see if the field is really right for me and as a way to beef up my admittedly anemic experience in the area for the sake of a potential PhD. 

But to be honest, I'm not sure of my prospects of getting into a good master's program. I feel like my lack of background will hurt my chances significantly. Although there is a little bit of overlap with my Asian studies degree (the language skills would help if I wanted to pursue Buddhist studies, for example), I'm not confident there's enough there to demonstrate adequate knowledge and interest. Furthermore, I took more than a few of my humanities classes in undergrad pass/fail since I was being pushed so heavily down the path of STEM. Should I be doing something else before applying to programs? Do I even have a shot of getting into a good program? What's the expectation for applicants coming out of undergrad? Any and all advice would be deeply appreciated!
There is no reason not to try to do this and many reasons why you should. But the only valid advice will come from an admissions committee or a professor in the field who will look at your qualifications and goals. 

Be sure to present yourself in the most positive light relative to the new field, of course. 

There may even be advantages of your STEM background. Mathematics and CS, for example have applications in the humanities and the background can lead to many fruitful collaborations if you speak the language of both fields. 

But until you apply somewhere you have no idea of the possible outcome.