If bisexuals form the majority of people (not saying they do, but if they did) then a less judgemental society would mean more of those people having same sex relationships. That bit makes sense.
With regard to lesbians in particular being anti bisexuals, I think we have to look at how society actually is. A big part of being a homosexual is about being not attracted to the opposite sex. The fact that door is firmly closed means so much of society is alien to us. As pp mentioned, all the stories, films and songs are aimed at other people, not at us. Couple that with discriminatory laws and abuse, and you get a siege mentality.
I'm not saying that to be inflammatory; it is a part of my own experience of the world. It's why gay and lesbian people value gay and lesbian resources. Even being able to sit in a gay pub, knowing there are other people like you, and only other people like you, there, is comforting.
Bisexual people have other options open and therefore have less of the siege mentality. Being left for a man is galling for many reasons, and lesbian women who have had it happen to them feel betrayed. In reality, it's just one of those things, and perfectly understandable when you look at the number of available lesbians versus the number of available straight men. I think Pew did a survey showing 90% of bisexuals are in opposite sex relationships, and I was surprised it was as low as 90%.
Women who have been with men, either as bisexuals or as late bloomer lesbians, often learn how to behave in a relationship and in bed in a different way to how lesbians who have never been with men do. All that can be unlearned, and a "gold star" lesbian is just fortunate, not morally superior. But there is a reason why lesbians in general are wary of bisexual women. I had to unlearn my own biphobia which was linked to some deep rooted internalised misogyny (overshare moment).
There are also lesbian relationships between partners who are not suited to each other that begin out of a lack of other potential partners and continue longer than they should for the same reason. If you're only attracted to and attractive to 1 or 2% of the population, max - and of that tiny percentage many are closeted or partnered or you just don't find them attractive or they don't find you attractive - there's a good chance you might find yourself single for longer periods than you'd like.
There are a million reasons why even if society is non-judgemental, people with the option to form opposite sex relationships will do so over same sex relationships. Conceiving children, the larger number of potential partners, whatever. So in reality I don't think we will see a huge number of additional same sex relationships no matter what society says.
Bisexual women have a hard time too; high levels of abuse from male partners, assumptions of promiscuity, pressure for threesomes etc. I can see why a lot of bisexual women keep their bisexuality to themselves. Until "society being less judgemental" becomes "men stop treating bisexual women as just kinky" then those women are likely to stay closeted.
Also, straight women have no reason to partner with bisexual men, either. There is no shortage of straight men, and men in general are pretty homophobic, so it's not unheard of for outwardly homophobic men to have illicit sex with other men. The "MSM" acronym is used by organisations like HIV charities to get around those men's reluctance to even refer to themselves as bisexual (or indeed closeted homosexual but in an arranged marriage - there are a fair few men in that category).
I think biphobia is something that needs to be addressed, I'm hoping the LGB Alliance do some work on it, because there are a lot of issues that get swept under the carpet and bisexuals have their own needs that aren't really covered by any organisation at the moment.