The Other and the One
Butler states her worry about how naming one's identity as gay or lesbian could lead to an othering effect because it differs from heterosexual individuals who do not need to come out or say that they are heterosexual because it is just assumed. This reminds me of the idea of the International Day of Women or Black History month in which certain groups and individuals are celebrated during this special period during the year. In a way, this is good because it brings to light issues that women and people of color face in their everyday lives, however it also creates the effect of othering because it reinforces the need for these people to have a "special" day when in fact every day should be "their" day.
This phenomenon of labelling can also create barriers between people that might not exist without the label. However, this creates a paradox because the act of not labeling oneself might lead to further stigma due to not bringing the topic of LGBTQ issues to public discourse.
Indeed, Butler brings a very nuanced critique of identity politics that goes beyond "This is why Trump won." In my interpretation, due to her twice having mentioned (through a Foucault quote, and then again in her own words) the political purchase potential of reifying categories of sexuality of gender as creating locations from which to gain said political/rights ground, her problem is with the paradox of which part of the "I" is excluded to constitute an identity, and problematizing of gender and sexuality itself, though apparently, as you say, she goes more in depth, so I think I may have missed that.
As such, she seemed able to set aside the paradox to some degree for political purchase, but to the degree that it causes worry in "division", I think there's more to be said about these categories evolve from "site from which to negotiate political purchase" to "site of othering". Arguably, this "othering" is being imposed upon them. I feel that equating the two relies on conflating one with the other: equating the political purchase of gays and lesbians (as well as bi, trans, queer+ in a contemporary context) with being inherently "opposed" to what is deemed "good" for the rest of the population.
I feel that justifications for withholding these rights is the real 'divider' here, and I say this because we have other sites of familial difference that simply contain "difference" rather than a politicized "superiority" or "inferiority". While there is still a lingering default ideal of "2 kids: one boy, one girl", having a mix of 1-4 boys and girls is at least MUCH less politicized as a site of politics and rights (at least in a Canadian context, though various Asian countries encouraging more child-bearing each have their own stories, to be sure, and having more kids, or none at all is, itself, a cultural taboo being contested) than defining oneself as gay or lesbian. I mean to say that there are multiple sites of familial difference that are NOT politicized that theoretically could be, and that creating the position of "gay" or "lesbian" as a political tool is a kind of *step* towards these differences becoming as equal, and then, thus (I think), as apolitical as having a different number of children.
I consider this as a necessary step, since whether we choose to define categories or not, there is taboo and inequality, and so I see the contesting of this taboo by creating categories (which is necessarily, I feel) from which to bargain equality is a crucial step en route to it being an apolitical point, and, hopefully, embracing Butler's post-modern conception of both gender and sexuality.
@Lianzhen I agree with yours and Butlers points on the worry of being othered. However at this point in time, I think recognizing these groups that are being othered is important for spreading awareness of the issues they face. We live in an educated circle where we are taught about social inequalities and issues pertaining to these groups of people, however there are many parts of the world where people are not being taught these social phenomena. I think staging these special days of recognition and creating a platform for these minority groups is an important first step to recognizing that the problems they face do exist, and that further steps are required in order for the groups to gain more stable ground in society.