Some of the "tetra" mentioned are not tetras technically speaking, as you may know; stores like to use the name "tetra" because most people have a concept (perhaps inaccurate
) of what a "tetra" is, so the fish is more likely to sell. White clouds are one frequently named a tetra, though they could hardly be further apart from the characins. White clouds are minnows, and manage in basic harder water but long-term they need cooler temperatures as it notes in our profile. Zebras are danios, and these also manage in basic water.
Of the true characin tetra, Pristella maxillaris is a good one for basic water; this species interestingly occurs in acidic and basic water in different parts of its natural habitat. There are some others that have been tank raised for several years now, like the neon, glowlight, etc., and "manage" in basic harder water. But not surprisingly, they either lack full colour, or develop more health issues, or die prematurely. I see no reason not to think this is due to the effect of stress from water parameters that are not "natural" to the fish, notwithstanding generations of tank breeding. But of course, this in itself has other detrimental issues for most of these fish, as science is now finding out.
There are some colourful cyprinids that can manage in basic water, you might want to glance through our profiles, as there are a couple included if memory serves me.