Can we keep this a short discussion?Certainly.
tl/dr: "Having the right to do a thing does not make it the right thing to do".
My concern would be that I wouldn't want the discussion to devolveAgreed. I don't want that either.
My concern has nothing to do with what organizations you wish to support. It has to do with the face Groups.io presents to potential users.
Groups.io is a product of global scope, and one presumably striving to be a reliable long-term service. In that light, I think that placing an advertisement for an organization based in topical U.S. partisan politics on an official (and prominent) page of the service is, at best, counterproductive.
(I realize that you're advertising to that group, not for that group, but in this context I think that is a distinction without a difference.)
In fact, it is off-putting to a large number of people (those opposed to that that organization's agenda) and at best distracting to a potentially larger group of people (those outside the U.S., or at any rate uninterested in U.S. politics). It drives a completely unnecessary wedge between people who would otherwise band together in an apolitical group.
For example, I run groups here related to my high school classmates, and to my children's PTA unit. The members of those groups undoubtedly hold a wide mix of political views. If some fraction of my group members feel uncomfortable using this service for reasons that have nothing to do with the agenda and content of my group then I have a problem running that group. In the case of the PTA group it is conceivable that PTA bylaws could be cited to prohibit me from running the unit's email list here.