If I had the phrase
two blond haired, blue eyed people
- would the comma be out of place?
- should I hyphenate "blond haired" and "blue eyed"?
There is a two-part test for adjectives:
(1) Can you replace the comma with the word and?
(2) Can you reverse the order of the adjectives and keep the same meaning?
If the paired adjectives fail the two-part test, then no comma is used. This shows that they must remain in a certain order to make sense. These are called cumulative adjectives.
If two adjectives modify a noun in the same way, place a comma between the two adjectives. These are called coordinate adjectives.
If the sentence passes both the two-pair test, then you have coordinate adjectives.
One never uses a hyphen to separate two adjectives. It's always a comma, and you decide whether to use a comma or not by the type of adjective you are using.
more examples:cumulative adjectives - no comma
coordinate adjectives - USE COMMA.
@Apoorva's answer primarily deals with the situation where two adjectives both modify the same noun, but in OP's specific case what we've actually got is two "adjectival phrases" (each consisting of an adjective+noun), both modifying the same noun (people).
As it happens, OP's particular sequence blond haired blue eyed is something of a cliched stereotype, with over 55,000 hits in Google Books.
Looking at just the first page of results there, all except one are for "blond-haired, blue-eyed". And that exception is a bit suspect, since it carries on with the words "smiling face" (IMHO, a face isn't really something that can be blond-haired). In short, use hyphens.
As regards reversing the order to "blue-eyed, blond-haired", of course this can be done, and it makes no difference to the surface meaning. But given the "set phrase" sequence is four times more common, using the "non-standard" sequence would probably be (slightly) noticed by many native speakers. Unless OP has some good reason for wanting to cause a slight "frisson" in the reader through atypical phrasing, I'd suggest sticking with the standard version.