And really, what the SFSS thinks is not particularly relevant to University policy here.
No, but LGBT and gender issues are some of the few exceptions where the administration doesn't flip off the SFSS. I don't think it unlikely that the administration will push for all on campus Greek life to be co-ed.
Even if the administration is okay with Greek life, any future SFU Interfraternal or Panhellenic Council will answer to the SFSS, just like UBC's IFC and PC answer to the AMS (as /u/skull_fraccture pointed out). And if the SFSS forbids single-sex fraternities and sororities, which I think they will do, the bigger fraternities and sororities will still not be able to be affiliated with the university.
UBC AMS Respectful Environment Policy:
This policy applies to everyone to whom the AMS provides services (including: members of AMS clubs, members of AMS resource groups, customers and members of AMS Constituencies)
...
“Discrimination” means making a distinction, whether intentional or not, based on enumerated grounds, relating to personal characteristics of an individual or group, which has the effect of imposing burdens, obligations, or disadvantages on such individual or group not imposed upon others.
“Enumerated grounds” means: race, colour, age, ancestry, citizenship, creed, national or ethnic origin, sex (including pregnancy), religion, marital status, family status, disability (physical and mental), sexual orientation, gender identity, union membership, and criminal conviction unrelated to employment.
SFSS constitution:
By-Law 21–Prohibition on Discrimination
1.The Society shall not discriminate against any person on any ground enumerated in the Canadian Charter of Rights and Freedoms or the British Columbia Human Rights Code.
And section 15 of the CCRF says:
very individual is equal before and under the law and has the right to the equal protection and equal benefit of the law without discrimination and, in particular, without discrimination based on race, national or ethnic origin, colour, religion, sex, age or mental or physical disability.
So, essentially, UBC will allow you to make an all-male or all-female club, but SFU will not, and that is the reason there is no Greek life here on campus.