Why 纹 is the wrong character to write for tattoo? I've only ever known tattoo (wénshēn) to be written as 纹身.
I was reading an article from 凤凰财经 yesterday called 猪躺着也能挣：一张纹身猪皮值百万.
What struck me, though, were all the comments on the article saying things like:

错别字，不是这个纹，小便没好好读书

and

文身的文写错了！！好么！！！！

Looking through ABC, Zhongshan Medical and even the Grande Ricci they all have:

纹身〔紋/--〕
wénshēn
tattoo / tattooing (MeSH) / Tatouer

(respectively).
MoE and 两岸 have entires for 文身 and note:

亦作「刺青」、「紋身」。

There seems to be a pattern here, though. MoE and 两岸 are Taiwan-based; 凤凰 is Hong Kong-based.
So where are the complaints coming from?
Let's have a look at 规范

动 在人体的皮肤上刺上文字或图案。
注意 不宜写作“纹身”。

Oh, there it is. Mainland-based 规范 is not happy with the 绞丝旁 here.
I have my hunches but what's the deal?
Why are some people so insistent that 纹 is wrong?
And who are these people?
They are purists. In the words of Steven Pinker:


  ...also known as sticklers, pedants, peevers, snobs, snoots, nitpickers,
  traditionalists, language police, usage nannies, grammar Nazis, and
  the Gotcha! Gang.


According to this article, 纹身 is accepted by a newer version of 《现代汉语词典》 as an alternative form of 文身.