A nice compromise would be to explain the Pantheon related tattoos and leave the more open/general tatoos without explanation.
I like the idea of Dalish lore not being complete. It makes sense for tattoos to be reevaluated, even if it might be 'heretical', as cultures and people evolve.
For those reasons, Traditional and Non-traditional tattoos would be a good compromise.
The main reason the Dalish exist, however, is to preserve their race's ancient lore and customs... For centuries, the Dalish culture has been fairly static and inflexible by design. I don't think most clans would be receptive to any non-traditional ideas, even small changes to the practice of vallaslin and the religious symbolism within the tattoos. I could see different clans having unique tattoos that represent the Creators, since they are spread out all across Thedas, but broadening the meaning behind the tattoos to allow for secular or artistic designs seems like too big of a change to ever be acceptable. If the tattoo isn't even a representation of a Creator, then I don't see any justification for it to be a mandatory practice anymore...
I could be wrong though. Supposedly the Dalish clans can vary in culture, although I haven't personally seen much of that... It's possible that Lavellan's clan is unusually progressive in certain ways... that would explain why these new tattoos are drastically different from what we saw in Ferelden and are so abstract that no meaning can be easily drawn from them. But again, if they don't represent the gods, I see no reason why they should be part of a coming of age ritual... If it's just art, then forcing members of the clan to get them seems pointless.