This is notoriously difficult. Buddhist teachers are extremely reluctant to criticise one another; you won't get a straight answer if you ask "Should I go on a retreat with teacher X?". Ultimately you have to rely on your own intuition, which makes it a bit of a game of dice.
> What if you are interested in secular meditation and do not believe Buddhism or other religions are truthful?
Good luck finding a secular meditation tradition with more than about 20 years of accumulated knowledge underlying it. Find a real teacher with a lineage; if your inclination is secular, discount the religious elements of the teaching you receive.
A secular mindfulness teacher has no lineage support-structure to support their teaching activity. And generally, they don't have the experience and insight that comes from practising a wide variety of techniques in addition to mindfulness.
Vipassana has been mentioned, in the article, and here in comments. Vipassana is a set of techniques for destroying the belief that you have an independent self. Not believing you have a self is itself a mark of psychosis. Vipassana is a form of mindfulness; but it's a big mistake to think that Vipassana practice can be secular. It's entirely founded on the (religious) view that belief in an independent self is the root of "suffering".