I'm experiencing the same thing with Malwarebytes 126.96.36.1992 / Component v1.0.390 / Update 1.0.5715, but I think I've narrowed down the cause somewhat.
Non-https sites don't load at all
Consistently broken across browsers
No filtering/blocking popups appear
With Web Protection enabled and AdGuard running, non-https websites don't load at all-- they just sit there with the status bar reading "waiting for <site>...". This occurs for every plain http site I've tried, but for a specific example: http://www.stealmylogin.com
I believe it's a conflict between AdGuard Pro for Windows (v6.3.1303.3881 - release branch), which decrypts TLS connections to do deep filtering, and a recent version of the Web Protection module
If I either disable Web Protection or quit AdGuard and its background service entirely, things immediately go back to normal. I'm not running any other antivirus or network filtering applications.
Based on the ESET discussion above, it appears a recent change to Malwarebytes is causing issues with other network-filtering applications, rather than anything introduced by AdGuard or ESET.
edit: Also, adding Malwarebytes as a filtering exclusion to AdGuard, and vice-versa, had no effect