This problem can easily be resolved using onTouchStart, onTouchEnd props of View component without using gesture responder methods.
So the modified code will look like
<View>
<View onTouchStart={()=>this.console("Button 2 Clicked")}>
<Text>BUTTON 2</Text>
</View>
<View
onTouchStart={()=>this.console('Button 1 pressed')}
onTouchEnd={()=>this.console('Button 1 released')}>
<Text>BUTTON 1</Text>
</View>
</View>
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