Capitalisation, other than at the beginning of sentences, or for proper nouns (or other such exceptions that might exist) generally either denotes a term of art, or illiteracy.
Posting in ALL CAPS, or italics, bold or underlining creates emphasis.
If the sign advertised "FREE PARKING" or even the more legible "Free Parking" as a stand-alone statement in big bold letters at the top of the sign, it would be hard[er] to argue that it only applied to paying customers.
There will almost certainly be case law that clarifies who is and is not a customer, and under consumer law, ignoring (or reflecting) the general rule of contra proferentem, ambiguity is to be determined in favour of the consumer.
As regards the claim that capitalisation does not change the meaning of words in English, as claimed by one of our more prolific sh*t -posters, other than compliance with the rules of grammar, perhaps he could tell us whether it matters whether the word "capitonym" is spelled with a capital "C" or a lower case "c". Not that I was questioning the meaning, but the implied emphasis.
