This interesting psak is really a current machlokes, according to the article, so it is really a triple interesting psak, as all sides of the argument are interesting..

Donating a kidney to patients in need of one has become a very popular chessed nowadays, especially in the Haredi community (though not limited to the Haredi community). Much of the popularity can be accredited to the work of an organization called Matnat Chaim that promotes and encourages such kidney donations. Obviously, kidney donations must follow the laws for organ donation, no matter what organization it is being arranged through.

The question was asked if it is permitted to donate a kidney when the recipient might possibly be a secular Jew. This is often the case as the majority of the time it is an altruistic donation with the donor not knowing the recipient. Ergo, the answer can be very influential on the future of kidney donation in the frum community.

The responses are based on the possibility of whether or not the average secular Jew has the status of a tinok shennishba, as per the Chzon Ish's decision.

Starting with the more straightforward responses first:

* Rav Gershon Edelstein responded that one is allowed to make an altruistic kidney donation without knowing who the recipient will be, because [most] secular people retain the status of "tinok shenishbu". They are considered as if having been held captive, meaning they never had the opportunity to learn, so their lack of observance is not considered a fault - sort of like a type of annus. Such a person, considered a tinok shenishba, does not obtain the status of a wicked person, even though he or she does not observe the mitzvos and even transgresses prohibitions publicly. Therefore, one could donate a kidney even if it will go to a secular Jew.

 * Rav Yitzchak Zilbershtein responded that one can, and should, donate a kidney even to a secular Jew. Rav Zilbershtein adds that often in such cases we see that a certain bond develops between the donor and the recipient, and when the donor is religious and the recipient is not religious the donation has the ability to have a positive impact and influence on the recipient and bring him closer to Judaism and to fulfilling God's will.

 * Rav Chaim Kanievsky is the most complex of the respondents. Rav Kanievsky normally follows the Chazon Ish, his uncle. But he also follows his father in law, Rav Elyashiv. And he also would direct many piskei halacha to Rav Shteinman rather than answering himself, until Rav Shteinman's death. While Rav Kanievsky seems to potentially be pulled in three different directions on this.

Rav Kanievsky paskens in this case like his father in law Rav Elyashiv, saying that secular Jews nowadays do not have the status of tinok shenishba because even if they never learned Torah and Judaism, the information is readily available to them via the computer (I will comment on this point below) and anybody seeking the truth will find a way to discover it. Therefore, according to Rav Elyashiv, secular Jews today do NOT have the status of tinok shenishba but that of a mumar - someone who intentionally sins against God.

Rav Shteinman paskened that secular Jews nowadays do continue to have the status of tinok shenishba. He reasons that there is so much incitement today against religion that no secular Jew can objectively decide he wants to research Judaism and come to the truth.

Rav Chaim Kanievsky, paskening like Rav Elyashiv on this matter, therefore says that one should not donate a kidney to an unknown recipient.
source: Israel Hayom

the debate is very complex and I would add another point that was not mentioned in the opinions brought above. Many secular Jews are even ignorant of the starting point and do not even know to look. They are not necessarily anti-Torah or anti-religion, but they were raised and live lives totally devoid of Jewish halacha and Torah considerations and remain oblivious to it. I am not comfortable with the opinion that they could look for the information if they wanted, thus they are responsible for not having done so, so to speak, because it isnt even on their radar. That's how far removed much of the secular community is.

I would add one point of irony in Rav Kanievskky's opinion as quoted. The information about Judaism might be available to the masses easily "on the computer", but Rav Kanievskly himself, supposedly, considers it a serious prohibition and transgression to use the Internet and smartphones and the like. Maybe they are fulfilling a mitzva following his opinion to not use the internet, even for good things!

I would add, regarding the point made by Rav Zilbershtein, that it irks me in particular, and I have written about this elsewhere, that anything we do in reklation to the secular community seems to have to have an ulterior motive of kiruv. Why must kidney donation be ok because it might possibly cause the recipient to do teshuva? Why cant it just be to save a life? Why do we invite people over and say hopefully it will cause kiruv - cant we just invite a friend to spend time with the friend or because I love my cousin or sibling? Sure, you can do things for kiruv purposes, but why does it seem to very often be the underlying motive in almost anything done in the frum community with the not-frum community?  To illustrate further, just the other day I was in a store. The woman before me in line was talking to the clerk about a wedding she is making for her child and she mentioned her two sisters coming in for the wedding that are not frum. She commented that she hopes they will come in and enjoy the wedding and it will hopefully be the start of them becoming frum. Can't they just be invited and come to the wedding because they are siblings, aunts and uncles and we all want to share our simchas with our beloved families? Must their invitation be for the purpose of kiruv?

caveat: as always, do not make a halachic decision based off a brief halachic review article you read on the Internet. If the situation is relevant to you, consult with a competent rabbi on the matter.