How to tell whether a stucco crack needs attention
Almost every stucco wall in New Mexico develops some cracking eventually. That does not make every crack equally urgent, and the difference is worth understanding before you decide whether to act now or wait. The useful signals are not really about width. They are about the edges of the crack, the wall around it, and where on the building the crack sits.
Look at the edges first
Run a finger along the crack. Clean, tight edges with the two sides sitting flush suggest the finish coat has parted without anything coming away. Edges that are chipped, crumbling, or sitting at slightly different depths suggest something is moving, or that water has already been working on the material from behind. The second case is the one that tends to get worse quickly.
Press the wall around it
Push firmly on the wall a hand's width either side of the crack, then further out. Sound stucco is hard and unyielding and gives a solid, dull sound when tapped. If an area feels soft, flexes slightly, or sounds hollow compared with the wall a few feet away, the finish has likely lost its bond with what is behind it. That is no longer a surface repair, and it does not improve on its own.
Note where the crack runs
Cracking that steps down and away from the corner of a window or door often reflects movement in the structure rather than the finish alone. Cracking concentrated near the top of a wall under a flat roof frequently points at the parapet cap above rather than the stucco you are looking at. Long horizontal cracks partway up a wall are worth mentioning to a contractor specifically. In each case the visible crack is a symptom, and repairing only the symptom tends not to hold.
Consider the season
Timing matters more here than in a milder climate. An open crack takes on water during monsoon storms, and winter nights across much of New Mexico cross the freezing point repeatedly. Water that has worked its way behind a finish expands every time that happens. A crack that looks minor in September is often wider by March, which is the practical argument for dealing with cracking before winter rather than after it.
When to stop guessing
If the edges are chipped, if any part of the wall feels soft or hollow, if there is staining running down from above, or if the cracking follows a stair-step pattern from an opening, it is worth having someone look rather than waiting another season. Describe what you have found in the quote form, including which wall and roughly where, and a local contractor will follow up to arrange a look.