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There's an inherent order to adjectives in English[0], so the sentence is objectively formed as "critical Danish infrastructure".

I do understand why someone would (knowing those rules) write "Danish critical infrastructure", possibly for emphasis, but it's not - and take this word very loosely - correct.

[0] https://www.gingersoftware.com/content/grammar-rules/adjecti...

I’m not sure quite how to read these rules - isn’t “critical” a “purpose or qualifier”? Which would mean the original formulation follows the rules.

No, a "purpose or qualifier" is (usually) the defining characteristic of a noun.

For example, power infrastructure vs water infrastructure. If you said "power Danish infrastructure" or "water Danish infrastructure", power/water don't make sense as adjectives.

Sometimes "critical" is a qualifier like "critical condition" but in this case, it's a quality.

I agree with it, how would you phrase it?

Seems fine as Danish critical infrastructure. Similarly French blue cheese, Prussian light infantry, American civil war.

As a native, speaker I am.