Looking at someone counts as "targeting" them (according to Jeremy Crawford)
Going purely by the rules as written, it's not clear whether protection against targeting by divination spells would protect you from spells that the caster casts on their self that then grant new senses, such as see invisibility or true seeing. However, Jeremy Crawford has clarified on Twitter1 that in such cases, you are still protected:
The nondetection spell hides you from divination magic. True seeing is a divination spell.
The nondetection spell grants a similar benefit to the Amulet:
The target can't be targeted by any divination magic
So JC's ruling should apply to the Amulet as well. This means that divination spells like true seeing will not enable a creature to see you, even if they don't explicitly "target" you.
Senses and abilities not based on divination magic function normally
As the other answers have covered adequately, the Amulet offers no protection against senses and abilities that are not based on divination magic. This includes the Robe of Eyes, unless your DM rules that this magic item is divination-based, which would not be unreasonable. It also includes creatures with a natural ability to see invisible things.
1 Note: JC's Tweets are no longer considered official rulings. I can't find this particular ruling in the Sage Advice Compendium, so it can be considered semi-official at best, hence the parenthetical qualifier in the heading.