The Eastern and Western Bluebirds were in serious decline due to habitat loss and large increases in the population of the invasive Starling and House Sparrow, and most US authorities do credit well-maintained Bluebird boxes as responsible for the resurgence of the species.
On legality: House Sparrows (along with European Starlings) are considered by US law to be an invasive foreign species and there are no federal prohibitions on trapping and humanely killing, disturbing the nests, removing the eggs, etc. of those birds. (All other wild birds are protected by international treaty and US law.) ("Active" control, such as trapping, may require state-level permits, but I'm pretty sure nest and egg removal is allowed everywhere.)
The routine monitoring of Bluebird nesting boxes is not considered "wildlife rehabilitation" for the purpose of requiring legal permits, as long as one does not actually touch the eggs or any birds except Starlings or Sparrows.
On legality: House Sparrows (along with European Starlings) are considered by US law to be an invasive foreign species and there are no federal prohibitions on trapping and humanely killing, disturbing the nests, removing the eggs, etc. of those birds. (All other wild birds are protected by international treaty and US law.) ("Active" control, such as trapping, may require state-level permits, but I'm pretty sure nest and egg removal is allowed everywhere.)
The routine monitoring of Bluebird nesting boxes is not considered "wildlife rehabilitation" for the purpose of requiring legal permits, as long as one does not actually touch the eggs or any birds except Starlings or Sparrows.