Passing an additional parameter with an onChange event

When you are writing this:

<fieldset onChange={this.props.handleChange("tags")}>

handleChange will be called immediately as soon as render is triggered.

Instead, do it like this:

<fieldset onChange={(e) => this.props.handleChange("tags", e)}>

Now the handleChange will be called when onChange handler is called.

In your handle event use double arrow function, there's no need to bind when using arrow function:

handleChange = tags => (event) => {
    console.log(tags);
    console.log(event.target.value);
}

And in the Child:

<fieldset onChange={this.props.handleChange("tags")}>
    <div>Tag 1: <input id="tag1" value={tags[0]} /></div>
    <div>Tag 2: <input id="tag2" value={tags[1]} /></div>
    <div>Tag 3: <input id="tag3" value={tags[2]} /></div>
</fieldset>