Diseases passed through blood
It is easy to see why many tattoo artists take issue with the notion that pregnant women should not get a tattoo due to the risk of diseases spread through blood, like Hepatitis B or HIV. If they know their equipment is absolutely sterile, what is the problem? Tattoo artists who don't use sterile equipment, or studios where you are not quite sure, should always be avoided regardless of whether you are carrying a baby.
Toxins in ink can pass to the baby
There is not a great deal of reliable information about the extent to which any potential toxins contained in the ink with which tattoos are made could harm your baby. Any toxins may be able to pass to your baby through the placenta, or they may not. When it comes to protecting your baby's health, it is best to err on the side of caution though. You avoid any chance of toxins passing through to your baby by not getting a tattoo during pregnancy.
When you are pregnant, your immune system is weakened and your body may respond to irritations like getting a tattoo in unpredictable ways. Your tattoo could look horrible because the ink may not take (actually, I once got a tattoo during my menstrual period and that one had to be touched up later). The site where you were inked may be more prone to infections as well, something that can be very nasty indeed, and may even land you in the ER.
Did you know it is actually illegal for tattoo artists to ink pregnant women in most states in the US? If you find a studio that will tattoo pregnant ladies, the chances are that it is not a reputable studio that cares about following regulations at all. Stay away! Believe me, I have thought about getting tattooed while I was pregnant. It may be petty, but I had a horrible tattoo and I didn't want my midwife to see it during labor and delivery! So I really wanted to get that covered with something else. But, getting a tattoo during pregnancy is just not worth the risk. No tattoo is stupid enough to put your baby at risk for.