I've heard back from Avaaz, the organisation running the petition. This is what they said:

Thank you for participating in Avaaz campaigns as well as writing to us to let us know that your friends weren't able to access the website.

It's frustrating to hear because the Indian government assured us that the ban on our website had been lifted and yet users occasionally do write to us saying they can't sign our petitions.

The way to fix this would be to contact your internet service provider demanding access to Avaaz.org. Your friends can use the information attached urging their service provider to give them access.

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Not that there's anything you can do, really, but that explains it not being accessible.