Mr.E is on a luxury spaceship travelling about 1/2 the speed of light and finds a cubic lump of unstable matter(attached to a bomb) in his cabin. He of course is an expert with bombs but this device is based on the unstable matter's critical mass. The lump of matter fluctuates a tiny amount constantly but if it is more than 2k.g, (say for the sake of argument) it will cause the bomb to explode. Right now it is at 1.9999k.g., if the ship accelerates making it over 2kg relative to the people anxiously monitering the ship from Earth they would think it should detonate yet relative to Mr.E and the fellow passengers its mass is still under 2kg?? Is this loose reasoning valid?
Critical mass is actually more about 'the right number of nuclei in a specified space'. As we are talking about solid matter this equivalently translates to a given number of atoms (or molecules depending on your matter). And this furthermore translates to our everyday mass. But it's 'not about mass', it is just a practical way to specify the quantity.
So in your example: It doesn't matter who sees how much mass. The question is whether is has the 'critical number of nuclei' in it and that doesn't change.
The bomb doesn't "care" what its mass might look like to an observer in another frame.
If you calculate critical mass you don't worry how big it might seem to observers located in billions of other possible frames of reference. Local frame of reference is the only one valid for making calculations concerning the occurence of local phenomena.