We don't log your IP address when the extension contacts our server but if you don't trust us you should use Tor or VPN. The extension can technically read any data from your BitcoinTalk session, including your PMs, but it doesn't do so. It collects user IDs from the page you're looking at - e.g. a list of posts in a thread - and sends that list of IDs to bpip.org to get info about those users, and only does so if you turn the optional features on (these features are off by default).
IMO, this is what I understood what Suchmoon said. The fact is that the extension can read all the data on the page you are viewing, but it only collects other forms of data, such as User IDs. It's not designed to collect data from PMs
The good thing is the code is open source. Anyone with some technical knowledge can help review it.