Hi, if you are on the latest version, 3.0, then open the app, tap the menu top left, see whitelist, tap that, then the plus button bottom right to load a list of your apps. Then select which ones to add to whitelist. That's it.
Hope you enjoy the app as much as I have. Although I strive to have only apps without advertising SDK's, I still need block-this on occasions. And I have also donated to the cause, which helps pay for costs. Help spread the word and another helpful app I use, is Sophos Mobile Security. Another free, ad free app, that is very comprehensive. Likely the only one left that is still free on playstore.
Also I would add Incase anyone else has this issue, that HTC added a new app to nougat update called "Boost+" and it can regulate apps in foreground and background. Open the app, then background, find the apps you want to be left alone, tap the app, then the third choice is "off". I'm not entirely sure if this is in addition to battery optimization, but whitelist the app there also.
I updated to nougat on HTC m9, Sprint a few weeks back, and I've not experienced anything like what you mentioned. I would reinstall BT and try again. Do you have any web filtering by an anti-virus app? What browsers did you experience this issue? I have 4 different browsers, Chrome, Firefox, Adblock Plus, and Brave. Non have had problems with browsing while on BT. One thing I did have to do after updating was to reset all app permissions, or actually I reset all app preferences and RE-enabled the permissions for each app. But largely I was having a battery drain problem, since fixed. I also re did my backups from "back up & reset" and automatic restore, just to make sure everything was fresh. Basically, I turn off then back on, which cleared the old out, and stored all new backup data.