You don't have anonymous tracking of your portfolio using this extension. This is quite de opposite.
You are sending requests for those addresses to blockchair.com server, and they linking those addresses to your IP in their database.
You 100% identified and linking different addresses together.
Just to illustrate, you are basically visiting a URL with an address to get its balance:
Request URL: https://blockchair.com/bitcoin/address/tx-data?privacy-o-meter=true&address=1CHAriTyyuCzLdXshSDVohyjgxTxW9Bhx&hashes=&advanced=0&offset=0
Then they have a data with the list of URL you visited, and the IP from which you visited.
The only way to have anonymity while tracking your portfolio is by running your own full node (where you don't send requests to anyone requests your addresses balance) or using a tool such as loycev's all addresses with balance: https://bitcointalksearch.org/topic/list-of-all-bitcoin-addresses-with-a-balance-5254914 (as you get all addresses, he doesn't know which one is yours).