The restrictions around tattooing and blood donation are to do with transmissible diseases; essentially, they make you wait a year in case you contract a blood-borne disease because by then you would have become symptomatic and hopefully be aware that you should not donate.

I suspect the restriction on tattooing pregnant women is simply to do with legalities; the same reason pregnant women can't do a lot of things, in case something happens to the pregnancy and they think that the tattoo had something to do with it and sue.

And there is also a fair bit of body shape change going on during pregnancy so tattoos might end up not looking as planned!

As far as I am aware, if you are willing to accept the risk of blood-borne disease, there is no reason why you cannot BF and have a new tattoo, but I'd definitely pay the big money and go somewhere reputable and clean.