Harvard to Sanction Final Clubs, Greek Organizations
thecrimson.com
thecrimson.com
The first amendment is a protection against state harassment, it does not mean private entities are obligated to continue their relationship with you.
For a less sinister example: if you work in a newsroom and your name shows up on a political party registration list or any kind of political donation, you're fired.
This is very much state harassment, since its ultimately coming from the Department of Education's enormously broad interpretation of Title IX.
For example, here's a list from a bit over 10 years ago of journalists who are registered with a party and made political donations. http://www.nbcnews.com/id/19113455/ns/politics/t/list-journa... . For examples of places which did not strictly prohibit donation (in 2007): "The NBC policy does not outright allow or forbid donations but requires approval of the president of NBC News", "Msnbc.com policy requires permission of the editor in chief for any political activity", "Forbes has no policy regarding employees' personal contributions to political parties or candidates, but it does encourage any employee to be involved in their communities in any way they choose" and "Fox does allow news employees to make political contributions."
Furthermore, there are other exceptions. 1) the newsroom must not be run by the government (eg, Voice of America), 2) non-federal law may still prohibit political affiliation discrimination. The District of Columbia Human Rights Act prohibits discrimination on the basis of political affiliation, meaning "the state of belonging to or endorsing any political party." I think the Unruh act is California is similarly broad. I don't know if either has been tested in workplace employment matters.
http://www.humanrightscommission.vic.gov.au/index.php/workpl... suggests your example would be illegal in Australia.
Many college administrations are pursuing a very contentious social agenda against single-sex private clubs, at the expense of students' liberties. A lot of it is driven by large SJW/"Safe Spaces"[1] contingents at these colleges. Fraternities and sororities are popular targets for those who hurl accusations of racism, sexism, etc. at every opportunity.
There's also a campaign in some parts of the media to smear these institutions by publishing unsubstantiated allegations. You might remember the article about an alleged gang rape by fraternity brothers and how it blew up in Rolling Stone's face. A few years prior they had a go at my own alma mater by publishing the lies of a disgruntled student who had several run-ins with the law, including an assault on a security guard (throwing a chair at her) and witness tampering in a case where he was originally charged with drug possession. As a result of all this, he was suspended from the college and expelled from his fraternity. That didn't stop the hacks at Rolling Stone.
It doesn't help that the leadership at universities is pitiful. At my college, part of the administration was happy to impose their political agenda by controlling student's lives and destroying any other poles of power. The rest were too scared to make a stand, lest the witch hunt turned to them.
[1] Does anyone have a better name for this movement? I really don't like "Social Justice Warriors". It's too ironic and dismissive, and detracts from serious critiques of the movement. "Safe spaces" just refers to part of their agenda, and parrots their Orwellian phrase.