While I was writing Victoria's responded and got it right. Here's my response anyway.
(as an aside, I don't get the Gallente dislike of tattoos. The Republic was formed 100 years ago, the adults that would have disliked them would be dead, and the youth that loved them would be the adults of today. CCP and their incapability of acute decade-by-decade culture shifts, I suppose)
Hmm, what dislike of tattoos? They are a pretty integral chargen option for Gallete characters, so that would be a tad odd.
The Gallente find the culture of tattoos somewhat barbaric and uncivilized, and early on tried to persuade their Minmatar neighbors to drop this old custom and embrace their future as a civilized nation. Their efforts to this end were initially met with polite denials and later with derision, but interestingly the Gallente youth now find the custom fascinating. Indeed, it is not uncommon to see young Gallente teenagers sporting tribal and gang motifs lifted from their Minmatar peers, symbols of whose true meaning they have little to no knowledge. This can evoke anything between high derision and outright hostility when those so inked encounter true Minmatar.
I read this as a statement about cultural conflict over individuality. To Matari, tattoos show your place in the culture and society, and are not chosen by the individual. To Gallente they're an individually-expressive form of body art.
[....] a Minmatar’s tattoos proclaim who he is, where he came from, what he does, where he has been and what he has experienced. They represent a Minmatar's identity as well as his story. A Minmatar without his markings is not considered a Minmatar at all.
[....]
After the Voluval ceremony the young Minmatar will receive her permanent naming mark which will reside forever on her face. This mark will identify the name, clan and tribe of that Minmatar, plain for all other Minmatar to see. In such a way, two Minmatar meeting for the first time can immediately know these fundamental specifics about each other.
[....]
A Minmatar cannot bestow upon herself just any tattoo. In some cases she may be able to influence styling and shape, but she cannot add a tattoo without having first earned the right. Inking a tattoo upon yourself without permission is considered a grave crime and offenders are subject to severe judicial punishment.
In the Matari practice, tattoos show important aspects of who you are based on things most Matari don't individually control, such as their name, clan, tribe, and their voluval mark. I see this as quite alien to an ethnic Gallente strand of thinking that "we are all precious individuals and we can reinvent ourselves at any time regardless of where we came from". So it's precisely the 'tribalness' of tattooing that's most important to Matari and most awkwardly uncomfortable -- even barbaric -- to Gallente.
Tattooing as a means of self-expression seems to me to be a good fit with what we know of Gallente. A bit more permanent than Mannar-style body painting, sure, but with the modern laser-removal processes also mentioned in the chronicle you can still reinvent yourself when you feel like it.
And the Gallente getting punched in the face "inexplicably" for wearing a tattoo to which s/he has no right...? If they were in the Republic it's possible that they'd be facing local justice for it. (Which raises whole other questions about that would relate to visitors, residents and "aliens", or whether Gallente are just non-starters for involvement in the tribal justice systems and must always turn to Republic justice.)