The warning tells you what exactly you need to do. You cannot nest <p> tags and hence use div for the outer tag like
<div>
{this.state.error &&
<p className="errorText">
{this.state.error}
</p>
}
</div>
<div>
{this.state.error &&
<p className="errorText">
{this.state.error}
</p>
}
</div>