Please see the following brief video:
The very fact that Kagan's sexuality is being questioned, and being speculated upon using crass stereotypes, is akin to questioning and speculating upon her eye color vis a vis her suitability for the job of Justice on the U.S. Supreme Court!
The only possible speculative issue concerning her sexuality is that if she is a lesbian and is in the closet, she might well vote against LGBT rights, as do so many self-loathing closet cases, to keep herself more firmly ensconced in that closet. If she is not a lesbian, she is a wild card who might well vote against LGBT rights, feeling no affinity for LGBT people.
Indeed, she has stated: "There is no federal constitutional right to same-sex marriage," (See here..) she also stated in memos to faculty and students at Harvard that the military's policy of excluding openly gay men and women from serving is "a profound wrong — a moral injustice of the first order." (See here.)
So, if she's consistent in her views on these matters, we can expect her to approve the repeal of DADT, but follow the lead of Obama's Justice Department and affirm the constitutionality of DOMA.
And if she is a lesbian and comes out of the closet, she could well vote against LGBT rights in an attempt to show "impartiality."
So, really, her sexuality is largely irrelevant, especially for purposes of speculation, save for whether or not she is being honest and living an honest life, which relates to her character, the most important feature of any human being, especially one in the capacity of Justice of the U.S. Supreme Court.
So, in any case, especially not knowing much about her, she can be seen as a wild card on the Court, her sexuality notwithstanding.
In other words, her sexuality really tells us nothing about how she will vote on LGBT rights issues anymore than it will tell us about her judicial philosophy, about which we know absolutely nothing, as she has never served in any judicial capacity.
It is this latter fact which should be of concern to all thinking people, well over and above what her sexuality may be as speculated upon and targeted by some idiot pundits who are featured in the media, and in such foolishness as seen in the above video.