Ripe means (1) fully mature, (2) fully prepared to undergo something, and (3) smelly. Rife means abundant. When you see the phrase ripe with, the writer has likely used ripe in place of rife (though there are exceptions, such as where ripe means smelly—for example, ripe with stale curry).
The use of ripe in place of rife is a surprisingly common error. For example, each of these writers apparently means rife, not ripe:
The bay system is ripe with fish. [Houston Chronicle]
Joseph said he read the affidavit in full for the first time on Monday, and said it was ripe with falsehoods. [Standard Speaker]
But too many see theirs as soap operas, as bizarre and unbelievable and ripe with drama. [The Virginia-Pilot]
This confusion is so common that we should probably accept that ripe has a new, secondary definition making it synonymous with rife. It seems people like to use ripe in place of rife when the abundance is a good thing, and they reserve rife for negative abundances. But of course, rife in its traditional sense can be either positive (as in the last example below) or negative.
These writers use rife in its conventional sense:
Fuelled by countercultural rampant royalists across America, cyberspace was rife with its own take on the wedding. [Independent]
The muddy south bank of the James River in Richmond is rife with memories that were kept secret for years. [Washington Post]
This particular vintage – eminently quaffable and rife with layers of peach, apple, and lemon – was quite reminiscent of an Italian Pinot Grigio. [Star-Ledger]