Extending RssReaderWebPart SPFx web part to use 'rss-parser' module to render RSS feeds.

rss-reader-web-part-using-rss-parser.js

// Step-1: Add 'rss-parser' module as a dependency to package.json and import it inside RssReaderWebPart.ts file
import Parser from 'rss-parser';

export default class RssReaderWebPart extends BaseClientSideWebPart<IRssReaderWebPartProps> {
    // Step-2: Add a new private loadRSSFeedAsync() method inside RssReaderWebPart class of RssReaderWebPart.ts file
    private loadRSSFeedAsync(): void {
        (async (properties, domElement) => {
            const parser = new Parser();
            // Note: some RSS feeds can't be loaded in the browser due to CORS security.
            // To get around this, you can use a proxy.
            const CORS_PROXY = "https://cors-anywhere.herokuapp.com"
            parser.parseURL(`${CORS_PROXY}/${properties.feedUrl}`, (err, feed) => {
                if (!!err) {
                    // Log error message to console
                    console.error(`[RssReaderWebPart.loadRSSFeedAsync()] => ${err}`);
                }
                else {
                    if (!!feed) {
                        // Build RSS feed markup by iterating RSS feed items
                        let rssContent = ``;
                        rssContent += `<ul>`;
                        let maxCount = properties.maxCount < feed.items.length ? properties.maxCount : feed.items.length;
                        for (let i = 0; i < maxCount; i++) {
                            const item = feed.items[i];
                            rssContent += `<li>`;
                            rssContent += `<a href="${item.link}">${item.title}</a>`;
                            // TODO: Code for rendering description, publishing date...
                            rssContent += `</li>`;
                        }
                        rssContent += `</ul>`;

                        // Insert content of RSS feed markup into DOM
                        domElement.innerHTML = rssContent;
                    }
                    else {
                        console.warn('Feeds are not available!');
                    }
                }
            });
        })(this.properties, this.domElement);
    }

    // Step-3: Invoke newly created loadRSSFeedAsync() method from render() of RssReaderWebPart class inside RssReaderWebPart.ts file
    public render(): void {
        // Fetch RSS feeds and insert its content into DOM
        this.loadRSSFeedAsync();
    }
}