No, you can't trust NIST on security. They've certified algorithms they must have known were deliberately weakened in every generation: DES in the 1970s, the Clipper chip in the 80s, "export-grade" RSA in the 90s, and broken RNGs in the 2000s.
The deliberate weakening generally comes from the NSA, but NIST is required to work with them on security standards.
A number of reputable security researchers claim that NIST's misdeeds were all unintentional and they've learned their lesson and there won't be any more backdoors. Perhaps. Ultimately they serve the US administration, so in the long term it depends on whether future administrations actually want everyone to have unbreakable cryptography. Doesn't seem like a safe thing to count on.
The deliberate weakening generally comes from the NSA, but NIST is required to work with them on security standards.
A number of reputable security researchers claim that NIST's misdeeds were all unintentional and they've learned their lesson and there won't be any more backdoors. Perhaps. Ultimately they serve the US administration, so in the long term it depends on whether future administrations actually want everyone to have unbreakable cryptography. Doesn't seem like a safe thing to count on.