I have no idea what Wangguard does or how it works so a comparison cannot really be made between Wangguard and BPS. What would need to be looked at is how ClassiPress does what it does on the Login page – WordPress Hooks – Actions and Filters and compare that to BPS. The general rule always applies in cases where 2 plugins or plugin features are doing the same thing or a very similar thing – they will compete – that is completely normal/natural and typically you turn off the competing feature in the plugin or theme that you do not want to use so that you can use that feature in the other plugin or theme. Basically you cannot have 2 plugins or features doing the same thing. There is only 1 steering wheel on a car for a reason. ;)
If you want us to test the ClassiPress theme then send the zip file to info [at] ait-pro [dot] com. If the theme requires activation then provide us with that activation key. Upon completion of testing we delete premium plugins or themes and anything else that is private/personal/license oriented.