WordPress Minify HTML – functions.php From http://fastwp.de/snippets/html-minify/

wordpress-snippets-html-minify.php

<?php
class WP_HTML_Compression {
    protected $compress_css = true;
    protected $compress_js = true;
    protected $info_comment = true;
    protected $remove_comments = true;
 
    protected $html;
    public function __construct($html) {
      if (!empty($html)) {
		    $this->parseHTML($html);
	    }
    }
    public function __toString() {
	    return $this->html;
    }
    protected function bottomComment($raw, $compressed) {
	    $raw = strlen($raw);
	    $compressed = strlen($compressed);		
	    $savings = ($raw-$compressed) / $raw * 100;		
	    $savings = round($savings, 2);		
	    return '<!-- HTML Minify | http://fastwp.de/snippets/html-minify/ | Größe reduziert um '.$savings.'% | Von '.$raw.' Bytes, auf '.$compressed.' Bytes -->';
    }
    protected function minifyHTML($html) {
	    $pattern = '/<(?<script>script).*?<\/script\s*>|<(?<style>style).*?<\/style\s*>|<!(?<comment>--).*?-->|<(?<tag>[\/\w.:-]*)(?:".*?"|\'.*?\'|[^\'">]+)*>|(?<text>((<[^!\/\w.:-])?[^<]*)+)|/si';
	    preg_match_all($pattern, $html, $matches, PREG_SET_ORDER);
	    $overriding = false;
	    $raw_tag = false;
	    $html = '';
	    foreach ($matches as $token) {
		    $tag = (isset($token['tag'])) ? strtolower($token['tag']) : null;
		    $content = $token[0];
		    if (is_null($tag)) {
			    if ( !empty($token['script']) ) {
				    $strip = $this->compress_js;
			    }
			    else if ( !empty($token['style']) ) {
				    $strip = $this->compress_css;
			    }
			    else if ($content == '<!--wp-html-compression no compression-->') {
				    $overriding = !$overriding;
				    continue;
			    }
			    else if ($this->remove_comments) {
				    if (!$overriding && $raw_tag != 'textarea') {
					    $content = preg_replace('/<!--(?!\s*(?:\[if [^\]]+]|<!|>))(?:(?!-->).)*-->/s', '', $content);
				    }
			    }
		    }
		    else {
			    if ($tag == 'pre' || $tag == 'textarea') {
				    $raw_tag = $tag;
			    }
			    else if ($tag == '/pre' || $tag == '/textarea') {
				    $raw_tag = false;
			    }
			    else {
				    if ($raw_tag || $overriding) {
					    $strip = false;
				    }
				    else {
					    $strip = true;
					    $content = preg_replace('/(\s+)(\w++(?<!\baction|\balt|\bcontent|\bsrc)="")/', '$1', $content);
					    $content = str_replace(' />', '/>', $content);
				    }
			    }
		    }
		    if ($strip) {
			    $content = $this->removeWhiteSpace($content);
		    }
		    $html .= $content;
	    }
	    return $html;
    }
    public function parseHTML($html) {
	    $this->html = $this->minifyHTML($html);
	    if ($this->info_comment) {
		    $this->html .= "\n" . $this->bottomComment($html, $this->html);
	    }
    }
    protected function removeWhiteSpace($str) {
	    $str = str_replace("\t", ' ', $str);
	    $str = str_replace("\n",  '', $str);
	    $str = str_replace("\r",  '', $str);
	    while (stristr($str, '  ')) {
		    $str = str_replace('  ', ' ', $str);
	    }
	    return $str;
    }
}
function wp_html_compression_finish($html) {
    return new WP_HTML_Compression($html);
}
function wp_html_compression_start() {
    ob_start('wp_html_compression_finish');
}
add_action('get_header', 'wp_html_compression_start');
?>

Great function!
But, same issue, didn't work in PHP 7.

Using ob_start() in your website without having it encapsulated in a function means that it will run on every single page load when your plugin is active. That means you've just broken caching for everyone because the way PHP Sessions work is they indicate the visitor using sessions is unique and should have a non-cached view of the website. This specifically breaks Varnish type caching.

This is a BIG issue for you. The gain of compressing HTML from your plugin will be LOST by the lack of caching.