As J.R. says, that construction is grammatical, and indeed required.
A bare adjective, or one modified by one or more preceding adverbs, goes in front of the noun. (I'm adding a determiner, many, to your sentence, to make the structure a little less ambiguous.)
Many angry people were protesting.
Many passionately and vociferously angry people were protesting.
But an adjective which has a complement cannot be placed in front of the noun; it must be treated as a reduced relative clause† and placed after the noun.
∗ Many angry with the high prices people were protesting.
Many people angry with the high prices were protesting.
If the adjective is modified it will carry its modifiers with it.
Many people passionately and vociferously angry with the high prices were protesting.
The same thing is true of any ‘heavy’ modifier with an embedded complement, such as a participle phrase or an adjectival preposition phrase:
∗ Many suffering from hunger people were protesting.
Many people suffering from hunger were protesting.
∗ Many from the surrounding villages people were protesting.
Many people from the surrounding villages were protesting.
As Laure says, the clause may be bracketed with commas. This changes the meaning, however: the clause is now ‘non-restrictive’ rather ‘restrictive’: being angry with high prices no longer defines the people who were protesting, it is an additional observation about them. A non-restrictive clause can be placed in other places:
Passionately and vociferously angry with the high prices, many people were protesting.
Many people were protesting, passionately and vociferously angry with the high prices.
∗ before an utterance marks it as ungrammatical.
† A reduced relative clause is one from which the relative pronoun and any immediately following copula have been deleted as unnecessary: who were angry with the high prices.
The problem is that grammar is somewhat tied to meaning here. The position of an adjective in a sentence depends on its role.
When used attributively (to describe a noun), as stated in other comments and answers, the adjective comes before the noun:
All navigable rivers are being patrolled.
If you say:
All rivers that are navigable are being patrolled. (Others are not)
This can become:
All rivers navigable are being patrolled.
At first glance this doesn't really seem to change the meaning since:
rivers that are navigable = navigable rivers
Edit: But...
When an adjective comes after the noun it describes (like in the 3rd example), it functions as a postpositive modifier. Changing the position of the adjective (relative to the noun it describes) may bring a slight difference in the meaning of the sentence (the meaning of the word itself does not change!). When used postpositively an adjective connotes an ephemeral quality, one that is present at the moment, but doesn't always have to be. On the other hand, the adjectives used attributively may express either an ephemeral or a permanent characteristic, depending on the context. The difference between attributive and postpositive use of an adjective is explained in more detail in (the middle of) this post and in the comments.
Only some adjectives can be used both attributively and postpositively (while retaining the same word meaning), and these are the ones ending in -able and -ible (such as navigable). (But not even all of those - see later: responsible).
To cover another aspect (this is where grammar kicks in again): if an adjective is used predicatively (in a pattern: subject + verb + object + complement (here an adjective)) it would be in a sentence like this:
Signalisation on the banks made rivers navigable. (Or something like that, I'm not really an expert on rivers).
The upcoming event made people excited.
The meaning of some adjectives (when used as modifiers) changes depending on whether they are used attributively or postpositively. Some examples are: concerned, responsible, present etc. Neither navigable nor excited are among those. Here the meaning of the word itself changes and the difference can be determined by checking the dictionary definitions.
Best Answer
There are two possible mechanisms that could explain the position of the adjective in the example sentences that you provided: postpositive adjectives and whiz-deletion.
When you apply an adjective to an indefinite pronoun, the adjective must be placed postpositively (after the indefinite pronoun):
Whiz-deletion refers to the removal of a that-is or which is from a sentence:
Note that you can't do whiz-deletion if you are left with just one adjective after the that is: the adjective must be moved in front of the noun:
someplace is an indefinite article, so this example must use a postpositive adjective: you cannot put nice in front of the indefinite article:
If you were to replace the indefinite pronoun by a noun, the adjective cannot be placed postpositively:
You cannot use whiz-deletion to remove that is from the sentence below, because there's only a single adjective after it.
In this sentence, any is an indefinite pronoun, so a postpositive adjective would have to go after it, and before the noun:
This sentence can therefore only be explained by whiz-deletion:
Note that, when the adjective is a subject complement, the adjective goes after the noun, though there is normally a verb in between them:
If the verb is a be-verb and the sentence is converted to a question, the verb is moved to the front of the sentence, resulting in a NOUN + ADJECTIVE sequence:
One other situation I can think of where you get NOUN + ADJECTIVE is after verbs like make (CAUSE TO BE), consider (OPINION), go (BECOME) and go (BE) which can take an object followed by an object complement, which is an adjective.