It's common for a site to load content stored on other sites, usually advertisements. If these ads allow scripts (not just pictures), then visiting the site makes you vulnerable to what's called cross-scripting attack - the site itself may be clean, but the web page makes your browser load potentially malicious scripts from another site. That may be what is triggering Malwarebytes.
That said, I usually turn the web protection "feature" off on anti-virus and anti-malware programs. It usually causes an unacceptable slowdown to web browsing. And some of the unscrupulous anti-virus companies have even used it to gather statistics on what sites people are visiting so they can sell the info to marketers. But I run a pretty intense gauntlet of ad-, script-, and cookie-blocking extensions on my browsers. If you're not running at least an ad blocker, I'd leave it on.