I figured it out. I’ll post my solution here for others to see.

Somehow the default MC4WP form had code that was messing up with the theme css.

Use this instead:

<p>
	<label>Email address: </label> 
	<input type="email" name="EMAIL" placeholder="Your email address" required />
</p>
<p>
	<input type="submit" value="Subscribe" />
</p>