is there such a thing as a sensor we can’t use on the robot.

as long as it is in compliance with the “no part may cost more than $400” and “the robot can cost no more than $4000” rules?

Mostly yes, but you need to really study the rules to be sure of your particular sensor. If it is not prohibited, it is allowed.

Lasers above class 1 are not allowed, and certain laser-based sensors use such lasers.

Other than that no common sensor specifically comes to mind at the moment that is forbidden. Did you have something particular in mind?

I appreciate your comments and knew about the lasers. I was thinking specifically about light sensors when I posted.

As long as a light sensor doesn’t have a light that blinds anyone (including other robots) and doesn’t contain any unsafe parts/components (and meets costing restrictions as you mentioned), then it is legal to use.