Should I (F26) break up with my boyfriend (M26) because he can’t stop texting and calling his ex-girlfriend (F26)?

I(F26) have been dating my boyfriend (M26) for 2 years. Recently my boyfriend’s ex-girlfriend (F26) texted me that last year my boyfriend told the ex-girlfriend that he wants to dip me and asked her repeatedly to break up with her boyfriend. She said he wanted a more “religious” girl (in our culture we do prioritize religiosity). She said that she told she would not go back to him even if she was single and that she’s currently in a committed relationship. She also said he contacted her over the summer and emailed her that “he almost drowned and was thinking of her.” She said she deleted this email and blocked him. Also two days after my parents invited him and his family to a restaurant for food (early oct 2023), he texted her again on his work phone asking how she is. She didn’t know it was his work phone so she asked him “who is this”. He told her he had a car accident and asked how she was. Then he sent an apology saying he should have not texted her. She blocked his work number. She has screenshots to prove that he texted her. When I confronted my boyfriend, he said he was egged on by his parents to send the last text because they all want him to marry a “religious” girl rather than me. The other two times he contacted her he said it was a “moment of weakness”. He said at this point he will never contact her again and no longer wants to be with her. I am skeptical because I believe he could still go weak for another girl. Should I breakup with him over this?

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TLDR: Boyfriends keep trying to call/text his ex-girlfriend with the intention of possibly getting back together with her. Should I break up with him over this?