It's not clear to me
"a dancing creature makes a Wisdom save"
Much has been made (see this answer by Joshua and the comments thereon by Toby Y.) of the grammar of "As an action, a dancing creature makes a Wisdom saving throw". I certainly agree that
The lack of a "must" from a sentence does not imply the existence of a hidden "can" or "may".
But on the other hand, the claim that "makes a save" necessarily implies a "must spend their action" would be made stronger if this particular phrasing was used in other places in the PHB where its use was unambiguous. By my count, however, "makes a [Ability] saving throw" is used just two other times, in Dominate Monster and Dominate Person:
Each time the target takes damage, it makes a new Wisdom saving throw against the spell.
On the other hand, the phrase "must make a [Ability] saving throw" is used 124 times in the PHB1. Clearly, if "must" was meant, it could have been said instead, as it was earlier in the same spell description, where the spell says:
A dancing creature must use all its movement to dance
but notably does not say "A dancing creature uses all its movement to dance". If the two meant the same thing, why not have the usage be standard across the spell?
If "makes" and "must make" really are equivalent in all cases, I think it is fair to consider why one is so much preferred over the other, at some forty-times-to-one. If the reason is that "must make" is more clear or explicit, then it should be at the very least admitted that the use of "a dancing creature makes a saving throw" is less clear than it could be. But perhaps there is actually a nuanced difference between them.
"makes" doesn't always mean "must make"
It is certainly grammatically sound to use "makes" as the equivalent of "must make", but that is not the only possibility and doesn't always match the context of the sentence. "Makes" can also mean "does make". For example, "The cobbler makes boots" won't often mean "The cobbler must make boots" - it is far more likely to mean "The cobbler does make boots." One can argue that in context "must make a saving throw" is the most reasonable interpretation for the irresistible dance spell, but that argument comes from the context, not from grammatical necessity.
Breaking free
When speaking of saving throws, there is some nuance between being forced to make a save to avoid some new harmful effect, and being permitted to make a saving throw to liberate oneself from an ongoing undesired condition. It is the second shade of meaning that is operating in Dominate Monster and Dominate Person - taking damage offers one the opportunity to save again and thereby free oneself of the charm effect.
Each time the target takes damage, it makes a new Wisdom saving throw against the spell.
In fact, 'saves (and checks) to free oneself' follow this pattern, where the condition that permits the save / check precedes the description. They can be read as an 'if-then statement'. If the dominated target takes damage, then it is permitted a saving throw. The targets of enchantments (like the dance) are permitted saves, while the targets of physical restraints are allowed checks in the same 'if-then' format. Here is entangle, for one example:
A creature restrained by the plants can use its action to make a Strength check against your spell save DC
If the creatures uses its action, it does make a Strength check.
Returning to dance:
As an action, a dancing creature makes a Wisdom saving throw to regain control of itself.
Might we read this 'if the creature spends an action, then it does make a Wisdom save'?
Tasha's Hideous Laughter offers an interesting example where both a required save and a conditional save are presented in the same sentence:
At the end of each of its turns, and each time it takes damage, the target can make another Wisdom saving throw.
Each turn the target must save, but if it takes damage, then it saves. For dance, the question is still whether the save is required (it must spend its action) or optional (if it spends its action, then it makes a save). I do see the 'must use' as a natural reading of the text, but I don't think it is clearly the only interpretation possible.
Must use its action?
There are many spells and abilities that force creatures to use their movement. Most spells that impose conditions which can be ended with actions, however, allow the creature to choose whether to attempt to do so (cf. control water, detect thoughts, ensnaring strike, entangle, Evard's black tentacles, maze, Ottiluke's freezing sphere, web). If irresistible dance really does force a character to use their action to break free, it would be the only spell in the PHB to do so, which should also give us pause for thought.
I'm not convinced
The spell, as written, may imply that the action must be spent to attempt the save, as others have ably argued. But given all the other context clues, I'm not convinced this is the intent. It certainly isn't a clear or unambiguous interpretation. My choice would be to turn it over to individual DM's to decide at their tables.
1In the descriptions of one racial ability (the Dragonborn breath weapon), twenty-one class features (four of the cleric's (Turn Undead, Read Thoughts, Radiance of the Dawn, Charm Animals and Plants), the druid's Nature's Sanctuary, five of the battlemaster's (Disarming Attack, Goading Attack, Menacing Attack, Pushing Attack, Trip Attack), four of the monk's (Open Hand Technique, Quivering Palm, Fist of Unbroken Air, Water Whip), four of the paladin's (Aura of Protection, Turn the Unholy, Turn the Faithless, Abjure Enemy), the assassin's Death Strike, the warlock's Dark Delirium, and the enchanter's Instinctive Charm, the necromancer's Command Undead), one effect of equipment (Basic Poison), one effect of travel (Forced March), one effect of damage (Death Saving Throw), one effect of being dismounted, the effects of 79 spells (Bane, Bestow Curse, Blade Barrier, Blight, Burning Hands, Call Lightning, Calm Emotions, Chain Lightning, Charm Person, Circle of Death, Cloudkill, Compelled Duel, Compulsion, Cone of Cold, Conjure Volley, Contagion, Control Water, Delayed Blast Fireball, Detect Thoughts, Disintegrate, Divine Word, Dream, Earthquake, Finger of Death, Fireball, Fire Storm, Flamestrike, Flaming Sphere, Flesh to Stone, Glyph of Warding, Hail of Thorns, Harm, Hellish Rebuke, Hypnotic Pattern, Ice Storm, Incendiary Cloud, Insect Plague, Lightning Arrow, Lightning Bolt, Magic Jar, Mass Suggestion, Meteor Swarm, Modify Memory, Moonbeam, Otiluke's Freezing Sphere, Ottiluke's Resilient Sphere, Phantasmal Force, Phantasmal Killer, Planar Binding, Plane Shift, Polymorph, Power Word Stun, Prismatic Spray, Prismatic Wall, Ray of Sickness, Scrying, Searing Smite, Shatter, Sleet Storm, Spike Growth, Spirit Guardians, Staggering Smite, Stinking Cloud, Storm of Vengeance, Suggestion, Sunbeam, Sunburst, Symbol, Telekinesis, Thunderwave, Tsunami, Wall of Fire, Wall of Ice, Wall of Thorns, Web, Weird, Wind Wall, Wrathful Smite, Zone of Truth), and four monster abilities (Giant Spider's Bite, Imp's Sting, Poisonous Snake's Bite, Zombie's Undead Fortitude).