Is it advisable to have both Gmail- and iCloud mail address?

Its your choice to have Apple ID as example1@icloud.com signed in Mac system preferences , however additional mail address say example2@gmail.com can be added in Mac system preferences > internet accounts , also it can be removed by clicking on subtract sign see the section - Stop using an account Use your Internet accounts on Mac – Apple Support

hagakyrkogata wrote:

Is it advisable to hav both gmail- and iCloud mail addresses. If not, how do I remove Google completely?

It's not a question of "advisable". You can have as many or as few email address as you want. I have a Gmail address that I use as my Apple ID. I also have an iCloud email address. And a work email address. Many years ago, when I did some online dating, I created a separate email address just for that. I have a friend who has a separate address she uses whenever she buys something online (this idea is brilliant!).

I would advise you not go crazy and have too many as it can end up being a lot to manage.

Its fine, there should no problem. Email address cannot get mixed they are separate always.

Where do you think you need to remove Google from exactly?