Some say intimacy with a breastfeeding wife spoils the milk or harms the baby. Is that true?

No; the Prophet ﷺ considered this matter and did not forbid it, because it does not harm the child.
In a narration of Muslim, the Prophet ﷺ said he had intended to forbid ghilah (intercourse with a breastfeeding wife), then found that the Romans and Persians did it and it did not harm their children (Sahih Muslim, Kitab an-Nikah). So intimacy during the breastfeeding period is permitted once postnatal bleeding has ended. The real concerns are usually the mother's exhaustion, hormonal changes that reduce desire, or becoming pregnant again too soon; breastfeeding does not necessarily prevent pregnancy. Discuss suitable birth-spacing methods with a doctor, and give the wife rest and help with the baby. See the question on intimacy after childbirth.