When you make an HTTP request for a website, you are making a direct connection between your computer and the targeted server. By doing this, you are providing them with your machine's public IP address, which can be used to determine your general location, and your Internet Service Provider (ISP). Although this can't be tied directly back to your exact location, it could be used maliciously if its finds its way into the wrong hands. With this in mind, it is preferable to not expose any of your personal assets to untrusted servers.
Running your web scraper on a computer that is far removed from your physical location, with some sort of remote access, is a good way to decouple your web scraper from your personal computer. You can rent Virtual Private Server (VPS) instances from various providers on the web.
Some of the more notable companies include...