One Slax user, with nickname dajiangtang, notified me regarding a problem of chrome module. It had root directory permissions set to 0744 instead of 0755. When such module was added to Slax root filesystem, it changed Slax's root directory permissions so unpriviledged (non-root) user couldn't login. That was actually just part of the problem, I got several other notices that after chrome module was activated, some other strange things started to happen.
I've fixed that and chrome module is rebuilt. If you had any troubles with Slax after using chrome module in the past, please upgrade to the new module now. Thank you for understanding.