ciao!

allora, ho modificato la classe come mi hai suggerito te:
codice:
class DialogBook extends React.Component {

    constructor(props) {
        super(props);
        this.state = {
            open: false
}
    }

    componentDidMount() {
        this.setState({open: this.props.open})
    }

    componentDidUpdate(prevProps) {
        if (prevProps.open !== this.props.open) {
            this.setState({open: this.props.open})
        }
    }

    render() {
        return (
            <div>
                <Dialog open={this.state.open} aria-labelledby="form-dialog-title">
                    <DialogTitle id="form-dialog-title">Subscribe</DialogTitle>
                    <DialogContent>
                        <DialogContentText>
                            Aggiungi
                        </DialogContentText>
                        <TextField
autoFocus
                            margin="dense"
id="name"
label="Email Address"
type="email"
fullWidth
/>
                    </DialogContent>
                    <DialogActions>
                        <Button color="primary">
                            Cancel
                        </Button>
                        <Button color="primary">
                            Subscribe
                        </Button>
                    </DialogActions>
                </Dialog>
            </div>
        )
    };
}

export default DialogBook;
poi dall'altro componente richiamo questa funzione:
codice:
function showDialog() {
    console.log('ok');
    return (
         <DialogBook open={true}/>
    )
}
in sostanza vedo il console.log, ma il dialog cmq non appare!