index.html

<script type="module">
    export default class RemoteContent extends HTMLElement {
        constructor() {
            super();
            this.parser = new DOMParser();
            this.shadow = this.attachShadow({mode: 'open'});
            this.append = this.shadow.appendChild.bind(this.shadow);
            this.shadow.innerHTML = 'loading…';
        }

        static get observedAttributes() {
            return ['url', 'selector'];
        }

        connectedCallback() {
            this.fetch(this.getAttribute('url'), this.getAttribute('selector') || 'body');
        }

        async fetch(url, selector) {
            let response = await fetch(url);
            let doc = this.parser.parseFromString(await response.text(), 'text/html');

            this.shadow.innerHTML = '';
            doc.querySelectorAll('link[rel=stylesheet]').forEach(this.append);
            doc.querySelectorAll(selector).forEach(this.append);
        }
    }
    customElements.define('remote-content', RemoteContent);
</script>

<remote-content url="https://ask-franklin.cloud.akeneo.com"></remote-content>
<remote-content url="https://developer.mozilla.org/en-US/docs/Web/API/Fetch_API" selector="h1,h2,h3"></remote-content>
<remote-content url="https://cors-anywhere.herokuapp.com/https://news.ycombinator.com/" selector=".athing"></remote-content>