The pledge calls on candidates in the Labour leadership race to back the expulsion of party members who hold "biogted, transphobic views".
It also describes Women's Place UK, a group which backs biological sex to be acknowledged as part of maintaining women's rights, as a "trans-exclusionist hate group".
Speaking on Sky's Sophy Ridge programme, Ms Nandy said the call for those who support organisations such as Women's Place to be kicked out of the party has given her pause ahead of signing the pledge.
"I have to say, that was the part of the pledge that gave me pause for thought about whether to sign it," said Ms Nandy.
"I decided to sign it in the end because I think that the sentiment of the pledge about protecting trans rights and about accepting that trans men are men and trans women are women is really important, especially at the moment with the level of discrimination that people face.
"I don't think that proscribing organisations is actually the right way to deal with disciplinary issues in the Labour Party.
"I think that the question for us is always about individual behaviour and it's right to recognise that there are women who have fought for generations in order to create safe spaces for women who want to have a proper debate about how we best protect that in an era where we've recognised that trans men are men, trans women are women, and we've got to do far more to protect trans women from harm as well.
"I want to see us have an open debate, I don't want to see us close down debate and I don't want anybody who's listening to this to think that I do."
Ms Nandy also suggested that pledge cards are being used to pit people against each other.
She said: "I think that pledge cards themselves have become a real problem in British politics and I think, with hindsight, if we could have all signed a pledge card at the beginning to say that we wouldn't sign pledge cards, we'd probably be in a much better place because one of the ways that pledge cards have been used is to pit people against one another.
"We've seen it happen with Brexit in recent years, we've seen it happen with the Israel-Palestine debate within the Labour Party in recent months and, actually, it surely must be possible for us to have a better level of debate than this."
Asked whether she would be happy for people who identify as women to stand on all-women shortlists, the Wigan MP said: "Yeah, I think that you have to walk the walk in the Labour Party and that means that we have to do two things - one is that we have to accept that people are who they say they are, I've never believed that politicians or even me as an individual should interfere or dictate to people who they are."
Speaking in an interview with the Observer on Sunday, Sir Keir Starmer called on Labour Party members to unite.
He said: "My message to our members is essentially that they've got a choice: we as a party can mope around, head in hands, arguing with each other, pointing fingers about who's to blame for this, that and the other.
"Or we could decide the next four years of our history is for us - we can pull together and shape what happens next."