Is a dentist unbothered by infection a red flag?

My partner got consults with two endodontists due to temp (cold) triggered pain. Both said old root canal was infected and required retreatment, but the 2nd said they also saw pulpitis in adjacent tooth and that was the real cause of the sensitivity. My concern is that the 2nd endo while thankfully noticing more was pretty nonchalant about the infection and said he’s seen people do just fine for years so it doesn’t necessarily need to be treated right away if patient favors focusing on the pain/pulpitis tooth.

A confirmed and unresolved bacterial infection (even if low level) seems way more problematic and risky than pulpitis. Should this be a red flag in choosing between the two endodontists?

Thank you so much for any feedback