I got a tattoo while breastfeeding after speaking to my (trusted) tattoo artist. There’s not much evidence that ink enters your milk supply, so he felt comfortable tattooing me. I think it’s mostly about the risk of infection, but he made a valid point that any wound can get infected and you’d still feed your baby as normal. I’ve also never had an infected tattoo. He was completely fine.
I feel there’s not enough research but some say it’s fine even to get tatted while pregnant. I think it’s your judgment. As long as the needles are sterile your risk is low. I think it’s more a “risk” if the needles are not clean then hiv, hep c etc