rigidly
In a stiff, inflexible way, without bending or changing.
Rigidly means in a stiff, unbending way, either physically or in how someone thinks and acts.
When something moves or stands rigidly, it doesn't bend or flex. A soldier standing at attention holds their body rigidly, with straight posture and no slouching. A frozen tree branch might snap if you try to bend it because ice has made it rigid.
The word more often describes how people think or behave. Someone who follows rules rigidly refuses to make exceptions, even when circumstances change. A teacher who rigidly enforces a “no late homework” policy won't accept your paper even if you were sick. A coach who rigidly sticks to the same game plan won't adjust when it's clearly not working.
Rigidly suggests an unwillingness to adapt or compromise. Someone with rigid beliefs won't consider new information or different viewpoints.
There's a difference between being consistent and being rigid. Consistency means reliably following important principles. Rigidity means refusing to think or adjust when you should. A person who rigidly insists on always doing things exactly the same way can miss better solutions.