A few things.
First, while there is no teaching allowing for or standing against tattoos, I would agree with the wise advice shared here by various persons: better not to do so, if simply to avoid making yourself a target. Your zeal is commendable, but better to hold off. It would be a completely different story if you were concerned about tattoos you’d accrued in your life, but you were asking about new tattoos (i.e. new action). Don’t pursue it.
Secondly, however, regarding the whole ‘your body is a Temple of the Holy Spirit’ response - For too long this passage has been thrown around; we’ve inherited our commentary on it from Protestant groups (as a former Protestant Bible scholar, I know

). The ‘you’ in 1 Corinthians 6:19 is ‘humwn’ - that is, ‘of you’ . . .
plural. This is further illuminated by the context: St. Paul is discouraging believers from taking out lawsuits against one another, and behaving (in
communio) like unbelievers. Basically, the you-plural - that is, the Church of Corinth, and by application the local participants in the universal Church - is the Temple of the Holy Spirit.
This is not to say that it wouldn’t be prudent to carefully consider what we do with our individual bodies, as they are indeed gifts from Almighty God. But to use this passage of Sacred Scripture as a denunciation of getting tattoos (or smoking, or drinking, etc.) is irresponsible and dishonest. I’m not berating the original user who quipped this; again, it’s a long, long inheritance that many of us (myself included) have fallen prey to in the past. I’m just going on the record here to correct this bizarre treatment of Sacred Scripture.
pax