Displaying publicly an egregious lack of taste is a halachik problem - in fact it probably qualifies as a chilul hashem (desecration of G-d's name) about which the general halachik rule is yehareg v'al yaavor (martyrdom rather than violation). Not to mention the emotional distress caused survivors or their descendents (as noted by Ray in a comment) is also a halachik problem (akin to onaat devarim - verbal persecution). As would be the empowering of antisemitism caused by diminishing the seriousness of the holocaust (just to name 3 issues off the top of my head).
In response to a comment, I add a source for the definition of chillul hashem:
See, e.g. http://www.nishma.org/articles/update/update5756-1.htm :
Basing himself upon T.B. Yoma 86a, Rambam states that if a pious
individual acts in a way that the general population would consider
inappropriate for this individual (and there is some inherent
legitimacy to this higher standard of behaviour and its imposition
upon this person), this person is performing a chilul Hashem. The
concern within this category does not seem to be the portrayal of a
lack of commitment to G-d. The concern seems to be the negative
portrayal of observance, that people will denigrate Torah in that this
pious person acts in such a negative way.
See also: https://www.ou.org/torah/mitzvot/taryag/mitzvah295/
This mitzvah applies to both men and women in all times and places. It is discussed in the Talmud in the tractates of Yoma (86a) and Sanhedrin (74a-b), and is codified in the Shulchan Aruch in Yoreh De’ah 157. This mitzvah is #63 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #155 of the 194 negative mitzvos that can be observed today in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.
See also: http://www.torah.org/learning/pirkei-avos/chapter4-5.html which is worth reading in full and relates the first and last example I gave of halachik issues in this type of behavior.