To answer this question, one just has to answer the question "Why don't they show nipples in PG-13 movies?"
Here a breakdown of X-Men movies, containing Mystique, and their age ratings, according to MPAA certification standards
* X-Men (2000) – PG-13
(Rated PG-13 for sci-fi action violence)
* X-Men 2 (2003) – PG-13
(Rated PG-13 for sci-fi action/violence, some sexuality and brief language)
* X-Men: The Last Stand (2006) – PG-13
(Rated PG-13 for intense sequences of action violence, some sexual content and language)
* X-Men: First Class (2011) – PG-13
(Rated PG-13 for intense sequences of action and violence, some sexual content including brief partial nudity and language)
* X-Men: Days of Future Past (2014) – PG-13
(Rated PG- 13 for sequences of intense sci-fi violence and action, some suggestive material, nudity and language)
* X-Men: Apocalypse (2016) – PG-13
(Rated PG-13 for sequences of violence, action and destruction, brief strong language and some suggestive images)
Directly from the MPAA Wiki:
Nudity is restricted to PG and above, although only brief nudity is permitted in a PG rated film. Nudity that is sexually oriented will generally require an R rating. As of 2010, the MPAA has added a descriptor of "male nudity" to films featuring said content.
Since only "brief nudity" is allowed, and female nipples are considered nudity, you can only get away with brief moments of nipple, like in the famous Titanic scene in which <PERSON> is nude, briefly.
Covering Mystique's nipple, but still being suggestively sexual/nude is allowed in a PG-13 movie.
The reason the producers and studio behind this film were aiming for a PG-13 rating with these movies is because all major superhero franchise movies have a tradition of aiming for this demographic. It wasn't until Deadpool (2016) broke the PG-13 mould for superheroes (which paved the way for the R-rated Batman v Superman cut (sold as the Ultimate Edition) and Logan (2017)).
An in-universe answer is that: she was electrocuted while being the conduit for two power cables.
After the success of the X-Men (2000) movie, <PERSON>, <PERSON> and <PERSON> created a mini-series of comics called "X-Men Forever", which explained certain unresolved plots, and more importantly, brought into the comic-book universe <PERSON>'s scaly appearance from the 2000 movie.
So now we can say that she may have had the blue nipples you're looking for, but they are hidden/scarred under the scales that the accident caused.
Note: the biggest hole in this in-universe explanation, though, is that the child version of mystique in First Class* (2011) also has these scales, which doesn't fit with the electricity accident explanation, which happened when she was an adult, but continuity errors and plot-holes are nothing new in the X-Men cinematic universe franchise. 387