I was struck by the following quotation, from Andrea Leadsom:
I find myself genuinely torn... I cannot vote against a measure that would mean so much to the minority of homosexual couples for whom marriage is the ultimate recognition for their genuine feelings for each other. Yet nor can I vote for a measure that risks centuries of faith based belief in marriage.
Remember, this is supposed to rationalise voting both for and against the gay marriage bill. First, she says that she cannot vote against it, though she did so. Then she says she cannot vote for it, though again she did so. True she might reasonably say she did not support the bill, nor oppose it, since by casting a vote either way her influence cancelled out. But she specifically says she could not vote either way, even though she did in fact vote both ways.
It's often said that to vote a particular way is to align oneself with it, which explains why people sometimes feel that they cannot vote a particular way with a clear conscience. Voting both ways isn't to align oneself unambiguously with either, but if voting sends any signal then she has to admit that she did vote for gay marriage (and against it). Perhaps, if she really felt that she couldn't vote either way, she shouldn't have voted at all.