The UK-based FS Magazine, a gay men’s health and life periodical, surveyed over 1000 “gay” men in Britain and discovered that:

“41% are in, or have previously experienced, an open relationship.”

More findings – of those men in an “open” relationship:
“93% strongly disagree that ‘open relationships are not real relationships.’”
“31% believe relationships end up open because gay men can’t be monogamous. However 47% think that it’s quite possible to have an monogamous relationship but choose not to;”
“Over two thirds of the men we surveyed who are currently in an open relationship said they don’t use condoms with their partner – although 64% say they always use condoms with casual partners. 55% have picked up an STI during their open relationship, with 70% believing they got that STI from a casual partner.”

This survey confirms the findings of these other more scientific studies:
“Ninety nine percent of couples reported having an agreement…Specifically, 45% had monogamous agreements, 47% had open agreements, and 8% reported discrepant agreements.”
Relationship Characteristics and Motivations behind Agreements among Gay Male Couples: Differences by Agreement Type and Couple Serostatus
Colleen C. Hoff, PhD, et al.
AIDS Care. 2010 Jul; 22(7): 827–835.

“Over half of the sample (66%) reported having established a sexual agreement with their main partner. Of these men, 47% reported ‘only sex with each other,’ 44% ‘sex together while with others,’ and 9% ‘sex with whomever whenever.’”
“Relationship Factors Associated with Gay Male Couples’ Concordance on Aspects of Their Sexual Agreements: Establishment, Type, and Adherence”
Jason W. Mitchell, Ph.D et al.
AIDS Behav. 2012 Aug; 16(6): 1560–1569.

“Some couples reported a change in the type of sexual agreement they had currently compared with when they originally established one. Specifically, over half of the men (63%) indicated that their original type of sexual agreement with their main partner was ‘We only have sex with each other and no one else,’ 34% reported ‘We have sex with each other, and we are allowed to have sex with others under certain guidelines/rules’ and 3% of the men chose ‘We have sex with each other, and are allowed to have sex with others without any guidelines/rules.’ When asked about their current type of sexual agreement, fewer men (56%) chose ‘We only have sex with each other and no one else’ while more (41%) selected ‘We have sex with each other, and we are allowed to have sex with others under certain guidelines/rules.’”
“Characteristics and allowed behaviors of gay male couples’ sexual agreements”
Jason W. Mitchell
J Sex Res. 2014; 51(3): 316–328.