Whenever I try to visit a link in a website, this popup appears, WTF???
the website you are visiting is requesting a client certificate and BTT's internal certificate (used e.g. for BTT Remote) is the only client side certificate you have installed, which is why Safari is offering it to you.
However if you receive this for all websites something is configured weirdly. This is not related to BetterTouchTool, but something might be trying to intercept your connection