I can answer this question for the EU, where the situation is similar.
Most, but not all so beware, of these new, online only, mobile first banks are legitimate in the sense that they are registered as banks and they are guaranteed up to 100k€. A few are working more as transaction facilitators, therefore they are not real banks and although you can use them as banks, you don't have the governmental guarantee. In my opinion, it would be a huge mistake to use such a transaction facilitator as a bank. You wouldn't keep all your wealth on your paypal, wouldn't you?
The real neo-banks can be trusted up to 100k€ as much as you trust your government that it won't default, so quite a lot. For anything above 100k€ you need to trust the bank itself, and trust is built over time. Since the whole point is that the neo-banks are new, I am personally not trusting any of them with large sums, above the governmental guarantee.
There is indeed an explosion of neo-banks and tech-fin in general, that is likely due to a combination of better internet (4G, 5G), the novel blockchain technology, and new client behavior caused by other technologies. There isn't enough space on the market for all of them to succeed though, so some will fail. Some of the traditional banks will also slowly adopt new features that are currently available only in neo-banks. I don't know which neo bank will fail, but I'd rather find it from a newssite than from an "access denied" when I want to check my account.
TL;DR; Trust them, but check they're real banks, and beware with large sums.