However, I would like to respond to this passage near the end:
So too, the possibility that a clearly Jewish attempt to seek enforcement of Noachide laws could result in vast antagonism and backlash toward Judaism from those groups whose conduct is categorically prohibited by Noachide law is not to be dismissed.
Yes, that may very well be, and discretion must always be used. But it is an unfortunate fact that the opposite position--practicing quietism while secular and heretical Jews identify Jews with secularism and immorality--can also create a backlash. A little balance to the latter behavior wouldn't hurt.
Well, the late Lubavitcher Rebbe had no such reluctance:
http://www.sichosinenglish.org/books/sichos-in-english/16/27.htm
...An integral component of the Jew’s task is to see to it that all peoples, not just Jews, acknowledge G-d as Creator and ruler of the world. The world, we are told, “was not created for chaos, but that it be inhabited.” A chaotic world results when there are no absolute criteria by which man lives, when morals and ethics are based solely on man’s understanding. Man is swayed by interests other than reason and justice; and we have only too recently seen the destruction which results when laws and philosophy are perverted to serve personal ends.
G-d, the Creator of the world, has not abandoned His handiwork, but has given clear guidance how the world can be made “inhabited,” settled and productive, decent and enduring. The nations of the world have been given a Divine code of conduct, the Seven Noachide Laws, which consist of six prohibitions against murder, robbery, idolatry, adultery, blasphemy, cruelty to animals — and one positive command, to establish a judicial system. These Seven Noachide Laws are general statements, which, with their ramifications and extensions, encompass countless details.
The reason these Seven Laws are to be observed is also important. The Rambam rules (Code, Kings 8:11) that the Sons of Noach (i.e. all humanity) must observe these Laws because “G-d commanded them in the Torah and informed us through Moshe that the Sons of Noach had already been so commanded.” A non-Jew conducts himself in consonance with the Seven Laws not because human logic compels him to do so, but because they are G-d’s commands transmitted through Moshe. This ensures that self-interest will never be allowed to pervert the Divine criteria of conduct.
It is through the observance of the Seven Noachide Laws that the entire world becomes a decent, productive place, a fitting receptacle for the Divine. Then, promises Scripture, “the glory of the L-rd will be revealed and all flesh together will see that the mouth of the L-rd has spoken.” The culmination of this will be the Messianic epoch, when, through the agency of Moshiach, “all will call in the Name of the L-rd and serve Him with a common consent.”...
A more specific statement:
http://www.sichosinenglish.org/books/sichos-in-english/35/06.htm
...there was a time when we did not reach out to the gentiles to encourage them to observe the Seven Noachide Laws. In the old days any attempt to discuss faith in G-d with gentiles would invariably lead to danger and even mortal danger for Jews. So, except for a few exceptions, there was no opportunity to fulfill this mitzvah.
In our generation things are different. There is no danger involved in this activity, and to the contrary, such activity will increase the respect that the nations show us, for they will realize that Jews care not only about their own welfare but also about the good of all humanity and the whole world...