See below

-- technology.lua

1) terminate the data:extend before nuclear-breeding technology is defined, by inserting the following:

})
if not mods["RealisticReactors"] then
data:extend({

2) before the final if statement (last line of the file), terminate this new data:extend and add a closing end, for the if:

})
end

This change will prevent the breeder technologies, if the "RealisticReactors" mod is installed. The breeder fuel cells do not work in the Realistic Reactors' breeder reactor, will only take Plutonium Energy's MOX fuel cells or uranium fuel cells.

3) Click the setting to disable the MOX reactor recipe.

Or if you have your own mod of mods script, you can add lines something like this:

if mods['PlutoniumEnergy'] and mods['RealisticReactors'] and data.raw['technology']['nuclear-breeding'] then
data.raw['technology']['nuclear-breeding'] = nil
data.raw['technology']['breeder-fuel-cell-from-uranium-cell'] = nil
data.raw['technology']['breeder-fuel-cell-from-MOX-fuel'] = nil
end

I don't like this solution and would rather explore other possibilities to bring breeder fuel cells into RR. IIRC it has a breeder reactor, so I will take a look at how it all can be integrated well.

They are working on a RR V4, no idea when that is expected, but they are making some adjustments too, I think.