How can a movement that claims to speak for everyone turn anyone away? Occupy Wall Street is struggling with how to police unwelcome elements as sex arrests, hate speech and activists pushing causes from the Chinese Communist Party to gas drilling threaten to muddle its message.

The fires and shattered windows at protests in Oakland, Calif., a sex assault arrest in New York’s Zuccotti Park and complaints of drug use elsewhere have drawn blanket statements from demonstrators against violence and unsafe behavior.

But to a large degree, the movement that welcomes everyone with a gripe against the system — any system — is embracing its fringe, saying protesters with causes unrelated to Occupy Wall Street are helping spur the revival of grassroots activism.

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