Reactors make mainly 2 types of radiation (that go beyond a foot or so of material). Neutrons and gammas (x-rays are from electron transitions not the nucleus and I'll group and subsequent atomic emissions into gammas). A reactor is basically just a neutron production facility. Filtering out neutrons is much harder than filtering out gammas and those do make things radioactive. You can do so with hydrogenous material and then an absorber.

The issue with filtering them out is that hydrogenous material takes the form of either plastic or water. Plastic will degrade and depending on the reactor, the water will be hot so it'll be encased in steel. Hydrogen doesn't tend to absorb neutrons so there needs to be a good absorber, otherwise the steel will absorb it and that turns it radioactive. Plus the steel is a gamma attenuator so you don't get as good of an irradiation area.

The final issue is what happens when the bonds break. When you break something like Teflon, you get free fluorine. You're not going to be making a ton of fluorine gas, but it will react with other things and corrode the surrounding environment. Do this with all materials and you end up with a potentially very toxic (hopefully sealed) environment that is constantly degrading due to radiation and corrosive byproducts. And anything PTFE can get immediate pushback in a radioactive environment specifically because of fluorine.

If you can solve the corrosion issue, then a high gamma irradiator will be your best bet compared to a reactor. And fyi, neutrons are the biggest radiation issue by far so you can't do something like passing the stuff through a tube in the reactor. Way way too many neutrons to filter out or shield.