The paradox is resolved when one considers the alteration of the basic paradigm between the two sources of lore: ED and the earlier FE2/FFE games.
In FE2/FFE, the Federation was essentially democratic in nature. The Corporations may have dominated the galaxy and been pulling the strings, but they were formally outside of the power structure of the Federation. In other words, the Federation had no "corporate members". All Federation Members were democracies, all Corporate States were Independent (like Sirius Corp).
With the rise of new ED lore, we see the Corporations now taking a much more active role in Federation governance. Not only are there Federation member-systems governed by Federation Corporations, but those government types come close to out-numbering the traditional Democratic government types. However, even these Corporations are governed by the Federation Charter, which presumably stipulates the core values which the Corporation must adhere to eg. "No Slavery".
This "Prime-Directive-like" attitude to protecting native lifeforms applied especially to lifeforms known or suspected of being sentient. Hence the whole bru-ha-ha around the extermination of the allegedly sentient pre-industrial lifeforms on Capitol, Achenar.
The Federation's abhorrence of exterminating native lifeforms came about by witnessing the relative ease with which all the native lifeforms of Taylor Colony, Tau Ceti, were exterminated and replaced with Earth-derived life. Having just survived a near-extinction-level event themselves (in the form of World War III), the 22nd century humans of Earth were very much in the "cherish all lifeforms" mentality. If one were to attempt to reconcile these two aspects of lore, then it seems reasonable that Federation Law requires Chartered Federation Corporations to abide by the Federation Charter in regard to native life protection.
Note that "protection" does not necessarily mean "prevention of exploitation" or "embargo on terraforming or colonizing planets with indigenous life". It is not required that Federation members must try to turn all planets with indigenous life into Galactic Parks. It is reasoned that the lifeforms can be "protected" with minimal impact on the profit margins, especially if the lifeforms are in some way exploitable. Apparently, so long as the native lifeforms don't actually become extinct, the Federation is OK with whatever you want to do to them. Federation corporations have since had a thousand years to perfect their "exploitation without extermination" modus operandi.
It is also possible that, as time passed and the memories of WWIII dimmed, and as the Federation explored more and more space and began to realise just how common extraterrestrial lifeforms were in the galaxy, they came to feel that life wasn't really all that special and didn't really need such stringent protection. Sentient life, however, was still rare, and retained the protectionist sentiment.
To the best of our knowledge, this "protect lifeforms" philosophy has not been manifested on the ground in the ED galaxy. Except, perhaps, for the inexplicable lack of colonies in the TRAPPIST-1 system - a star system which even early 21st century Earth-based astronomers knew contained colonizable planets likely to be host to native lifeforms. In ED, TRAPPIST-1 contains an ELW. Perhaps the early Federation explorers found suspected native sentient life there on that ELW, and the system has been off-limits to colonists ever since.
