Running own node = more anonymous?

Hello,

In many posts I can see the argument that running your own node can help being more anonymous, for example this post https://www.reddit.com/r/Bitcoin/comments/1cdow4i/dear_bitcoiners_start_running_your_own_bitcoin/

do you want anybody to realize the same IP keeps looking up the balance of the same address with that kind of balance?

I understand that, but I'm curious about another aspect. It is recommended to open port 8333 to truly participate in the network stability.

Doesn't that mean that anyone will be able to see that my IP is hosting a bitcoin node? Essentially it doesn't say that I am a bitcoiner but if we are realistic, how many people have a bitcoin node and are NOT interested in bitcoin?

There must be ways to hide somehow my IP or location, but does that require separate work/configuration, or is this integrated in the main tools available such as Umbrel or Start9?

Thanks!