Non-dismissible modal

A ModalView closes when it is removed from the React tree, and only then. Backdrop taps and the back button do not close it by themselves: they call onRequestDismiss, and it is up to that callback to update your state.

Close with your own button

Leave out onRequestDismiss. Backdrop taps and the back button then do nothing, and the modal stays until you manually unmount it, for example from a button inside the content or when an operation finishes.

import { useState } from 'react';
import { Button, Text, View } from 'react-native';
import { ModalView } from 'react-native-multiple-modals';

const ConfirmModal = ({ onConfirm }: { onConfirm: () => void }) => {
  const [isVisible, setVisibility] = useState(true);

  if (!isVisible) {
    return null;
  }

  return (
    <ModalView contentContainerStyle={{ justifyContent: 'center', alignItems: 'center' }}>
      {/* no onRequestDismiss: backdrop taps and the back button are ignored */}
      <View style={{ backgroundColor: 'white', padding: 20, borderRadius: 16 }}>
        <Text>Are you sure?</Text>
        <Button
          title='Confirm'
          onPress={() => {
            setVisibility(false);
            onConfirm();
          }}
        />
      </View>
    </ModalView>
  );
};

Full source: BlockingModal.tsx.