This sounds like good advice. My current employer does not allow me to write technical blogs or have public git repos even if they’re unrelated to work and when done on my own time with my own resources. Sigh.
That sounds like overreach; I don't think an employer is within his rights to try to restrict what you do in your free time with your own resources and without infringing on your employer's legitimate claims to IP (copyright, trademarks, patents, trade secrets, etc.)
This kind of overreach in contractual language and managerial posturing is somewhat common, driven by fears related to your exposure to your employer's IP, but the bark is worse than the legal bite here. I'm not a lawyer, but I still feel confident when saying that an employer wouldn't prevail in court, if they took legal action to enforce such restrictions on what you do outside of work.
The hilarious thing about their no open source policy is that they sometimes shoot themselves in the foot. Sometimes, they’ll hire someone with a very successful open source project, in the employment contract ask them to stop working on it, then part of the company depends on that software and when it breaks, it causes chaos because the maintainer now works at the company and had to stop working on that open source project that the company relies on.