From the Williams Institute:

A new study finds that lesbians, gay men and bisexuals (LGB) who sought mental health treatment from health care providers were no less likely to attempt suicide than LGB people who did not seek any treatment at all, but seeking help from religious or spiritual sources was associated with higher odds of a suicide attempt. The study, entitled, “The Role of Help-Seeking in Preventing Suicide Attempts among Lesbians, Gay Men, and Bisexuals,” is co-authored by Ilan H. Meyer, Williams Institute, UCLA School of Law, Merilee Teylan, Medical School, Harvard University, and Sharon Schwartz, Department of Epidemiology, Columbia University.

The study is the first to examine whether seeking various forms of mental health treatment is associated with lower odds of a suicide attempt in a diverse group of LGB adults. It finds that only about 16 percent of LGB people who made a serious suicide attempt sought mental health treatment from a health professional prior to the attempt; about 13 percent sought religious or spiritual treatment prior to the attempt.

The study finds that seeking treatment from a mental health or medical provider did not reduce the odds of a suicide attempt. Respondents who sought mental health or medical treatment at some time prior to their suicide attempt (or, among those who did not attempt suicide, prior to the age when suicide might have been attempted) were as likely as respondents who did not seek any mental health treatment to have a suicide attempt or serious suicide attempt after this time. However, counseling from a religious or spiritual advisor was associated with worse outcomes. Compared with individuals who did not seek help at all, those who sought help from a religious or spiritual advisor were more likely later to attempt suicide.

So seeking help from an actual mental health provider doesn't do any harm—and it doesn't do any good either (it doesn't reduce the odds of a suicide attempt for an LGB person)—but "seeking help" from a religious advisor or counselor makes an LGB person more likely to attempt suicide. No one could've predicted.