There are issues with some tattoos containing metals and MRI machines. Some of the pigments used to make brown and black colors are made up of iron oxide particles, they react to the machine and can cause a slight burn and you're not allowed to use an MRI then unless they cover it up. This is why before you go into an MRI machine, you are required to fill in a form that asks if you have any tattoos.
BUT
While there are still tattoo artists that use those pigments, there is a hard cap on the amount of iron oxide a tattoo can contain in the West. Pigments used should be organics based on carbon (with the exception of titanium white which doesn't react to MRI either).
Unless your tattoo was done in a foreign country, or by someone without a good reputation, your tattoo should not contain heavy metal particles. It does still happen, there are still reports of tattoos being done containing iron oxide pigments.
Why it's still done in foreign countries or by tattoo artists that want to save money, is because unlike carbon based organic pigments, iron oxide based pigments are the cheapest pigments that exist.
so in short, get your tattoo at a reputable place and ask if the tattoo artist uses organic pigments instead of iron oxide (there is no color difference between them, organics are just as colorful as their iron oxide counterparts)
Some people argue that it's rare that it happens even if your tattoo contains iron oxide, so it's not an issue, but that's a very flawed explanation, since the magnetic field and power of MRI machines has gone up considerably over the last years, and a 1.5 T MRI machine is much stronger than the MRI machines they had in the past, so over time, this could become a bigger issue.
