Since challenging homophobia is such a crucial issue, most out-bi people see it as politically vital to ally with lesbians and gay men.
It's often naïvely assumed that homophobia affects bi people only when they are in same-sex relationships. This is equivalent to suggesting that homophobia has no effect on lesbians or gay men who aren't currently in relationships. Bi people are just as likely as gay people to suffer from low self-esteem, internalised homophobia, and fear of the consequences of expressing their sexuality.*
Bisexuals living monogamously with an other-sex partner do to some degree escape the most dangerous or oppressive consequences of homophobia. This is sometimes suggested as the "easy way out". It does however depend on falling in love with someone of "the right sex" and not "the wrong sex".
Even while in an other-sex relationship, bi people may be hassled for looking gay on the street, or for taking part in gay activism or obviously queer social events. In many respects we still have to make choices about "how far out to be" that are similar to the choices gay and lesbian people face.
Clearly, when bi people are in same-sex relationships, they are in a position very similar to that of lesbians or gay men.
* See the Mind report "Mental health and social wellbeing of gay men, lesbians and bisexuals in England and Wales" for some related research. www.mind.org.uk.
In current western culture, bi people are frequently under pressure to deny one or other of the supposed "two halves" of our sexuality. This comes from gay and lesbian communities as well as from the mainstream.
The pressure is expressed directly in the way that other people are continually trying to assess which we "really" are and convince us of it. "But don't you think you're really gay and you just haven't come out properly yet?" "Oh, you're just dabbling in the gay world and then you'll go back to being straight", etc.
It's also manifested in phrases such as "sitting on the fence", "having your cake and eating it", "confusion", "can't make up your mind". The assumption is that we ought to choose "one or the other".
More subtly, bisexuality is simply erased by monosexist assumptions. Someone in a same-sex relationship is assumed to be lesbian or gay; someone in an other-sex relationship is assumed to be heterosexual. You can't come out as bi by simply being seen with any particular partner: you will virtually always be assumed to be either straight or gay, depending on the gender of the person you're seen with, unless you say otherwise.
Bi invisibility is linked both with homophobia and with the way that monosexism erases bisexuality. (Quite a few famous "gay" role models also have, or had, apparently significant relationships with "the" other sex.)
It also comes from the relatively recent development of a separate bi movement. In the early days of Gay Liberation, if you were bi it wasn't necessarily seen as important to make a big point of it - the important thing was liberation for all. (Hence an unfair stereotype of bi people as "coming along later to reap the rewards".)
Some people have suggested that the bi movement is about ten or twenty years behind the gay movement in terms of numbers and resources. Many people are still completely unaware that there's any such thing. Also, bi resources/businesses and support are relatively thin on the ground compared to gay and even lesbian community resources.
Straight people (e.g. governments allocating HIV prevention money) frequently assume that we're catered for by lesbian and gay resources. But lesbian and gay organisations haven't all welcomed bisexuals. Even when groups do officially welcome bisexuals in theory (which many now do), they don't necessarily have the perspective to see how bi people's needs may differ from what's already being provided.
Bisexuality has been a contentious issue in the past for lesbians and to a lesser degree gay men, and continues to be an issue from time to time. This can hinder alliances from forming.
Relevant stereotypes and ideas include: apolitical; unreliable; will return to mainstream culture when the going gets tough; have the best of both worlds; bi women will transmit HIV to lesbians; bi women will leave you for a man; bi women take energy from women and give it to men; bi women should live as lesbians in order to affirm their commitment to feminism, since they have a choice; bi men should live as gay since they have a choice; traitor.
Sexism, from gay men about women and from lesbians about men, can influence their view of bi people, if they see the bi person as somehow contaminated by the other gender.
While oppression from mainstream culture is undoubtedly more dangerous, many out-bi people feel that prejudice from the lesbian and gay communities is more painful, since it comes from people we perceive as similar to ourselves.
Many (though not all) bi people choose to live in non-monogamous relationships, so we have to deal with society's prejudices about that. Even when people are living monogamously, if they come out as bi they may well be assumed to be non-monogamous, since the idea that bisexuals always are is such a common myth.
Statistically as a group, we are more at risk of acquiring HIV than the average in the population. As with gay men, individual bi people are often assumed to be at high risk, regardless of the person's actual sexual practices.
The out-bi community seems to be pretty well organised when it comes to safer sex, and bi activists took the lead in some of the early safer sex awareness work in the US*; but behaviourally bi people who don't identify as bi or gay may well have very little access to information or resources.
* See, for instance, the interview with David Lourea in "Bisexual Politics: Theories, Queries & Visions", ed Naomi Tucker, which includes stories of AIDS awareness activism in the San Francisco area around 1980-1985.
It's clear that out-bi people are a small minority of behaviourally bisexual people, and an even smaller minority of people with attractions (not necessarily ever acted on) to more than one gender.* One issue that interests many out-bi people is how to reach those other people who might identify as bi, but have probably never considered it. Many of them have little or no contact with LGB culture and have no concept of a politicised sexual identity for themselves. If all those people identified as bi, queer politics would look very different.
* No-one knows how many people actually do have homosexual/bisexual behaviour in their history or present life; the "1 in 10" often quoted is a simplification of Kinsey's famous report, but his sample wasn't representative of the whole population of the US, let alone the world. Two other difficulties in research are (a) differences in definition, and (b) people not wanting to talk to researchers about their sexual activity. See http://www.kinseyinstitute.org/resources/bib-homoprev.html for a summary of some U.S. studies. The figures for "some homosexual activity" tend to range around 10% - 20%.
Most out-bi women are keenly interested in the intersection of bisexuality and feminism. A lot of bi men are fairly politically sussed about it as well although not all.
Some bi people feel they have a natural allegiance with queer &/or transgender activists who are interested in transcending gender categories, which obviously links with a challenge to some forms of sexism.
All in my opinion of course