The real answer to the actual question is, of course, No, it is not an *absolute* requirement. Only redundant gas is an absolute requirement, beyond normal dive gear (which includes a cutting tool, compass, timer/computer plus redundancy, etc).
Most of the answers are more about whether or not it is a good idea; Yes, most say. They argue a spare mask can be very useful, and is not hard to carry. This is in the category of moderate value-low effort, along with a spare light. The category of moderate value, high effort is things like a spare fin. The category of low value, low effort is a spare mouthpiece and cable tie. What you want to avoid is anything in the high effort category, unless it is possibly high-value: your redundant gas supply is in this category. So go through all the gear you need for a dive, and decide whether each piece is low, moderate, or high value, and is each piece, low, moderate, or high effort to carry as a spare? What about spare buoyancy, like a dual-bladder wing or a lift bag?