Yes...being exposed to a neutron flux in a critical reactor will kill you...quickly.
But to put things in perspective:
You have four cookies...a gamma cookie, an alpha cookie, a beta cookie, and a neutron cookie. You can eat one, hold one in your hand, put one in your pocket, and throw one away. What do you do?
Eat the gamma cookie...gammas have no mass, thus they are very low energy and do little biological damage, and are just as likely to pass through you without hurting anything.
Hold the Alpha cookie in your hand...your skin is dense enough to keep that particle out of your body.
Put the Beta cookie in your pocket...the fabric is dense enough to shield you from absorbing it.
You throw the neutron cookie away...it is high mass and high energy, and will do the most damage of any ionizing radiation.
With a reactor, all other fission products are contained within the cladding of the fuel pellets, and neutron levels fall very quickly after the reactor is shut down.
Clearly you are way over-qualified to be a GOP Senator.
And also 100% correct!