By "religious," do you mean "attends most holiday services," or "wacky paranoid Bible-waving End-Of-Times evangelical"? If more toward the latter then... no, just no.
I generally don't recommend announcing polyhood to the family.
Often, it's nothing but belated "teen rebellion," a way to make symbolic oppressors finally squirm a bit. Toss any sort of wild-eyed fanaticism into the mix & it looks like a bigger bear at which to poke a stick.
Been there, done that (re: making the oppressors squirm) decades ago as an actual teen.
Both my brother and I were variously kicked out of home, disowned, lectured and made examples of by our father for "crimes" such as leaving the church, unacceptable political affiliations, engaging in pre-marital sex/"living in sin" or having children out of wedlock.
My brother (who is bisexual) has often been involved in simultaneously intimate relationships over the years, but has never claimed poly status or made any big announcements. He keeps his private life on the down-low from family in general, especially our parents who tend toward religious conservatism.
On the other hand, I have historically been more open and "honest" (foolishly, who's to say?) about my personal life, even if that's left me open to parental judgement and condemnation.
I've only recently started to live by the tenets of ethical polyamory, however, and although I'm "out" to family and friends my generation and younger (my ex husband, siblings, children, their friends and my close friends all know), I am NOT out to my parents, and I intend to keep it that way.
At their age and stage in life (they're elderly and Dad has recently been diagnosed with dementia) they have enough issues of their own and quite frankly, I don't think they really care what we "kids" do anymore. I don't think this news would thrill them, even so, and I'd rather not give them more to fret about right now, so I'm choosing to keep this from them. IF they find out, they find out, and I'll deal with it then... but no, I don't think it's in anyone's interests to come out to them at this stage.
Every poly person (or gay, queer or whatever) has to make this decision for themselves however. Often it's a case of weighing up what will ultimately be the lesser of two evils: causing hurt and disappointment to parents vs temporary embarrassment of coming clean or being "found out"... or, at the extreme end of the spectrum, losing one's family of origin, but gaining the freedom that comes with living and loving authentically.