Is it possible to tell google to stop nagging me about chrome?
Solution 1:
I believe you're referring to this popup about Chrome (browser), not the one in your picture about Google (search engine).
I haven't come across a way to simply make Google remember my answer and stop asking me, but you can block it like any other ad with Adblock:
Click the ... in the upper right of the browser.
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Click Adblock
Click "Block an ad on this page"
Click the popup and drag the Adblock slider until it disappears
Click "Looks Good"
Solution 2:
Sorry to necro but this came up first when I searched for the problem so thought I'd post my solution.
I found if I disabled my ad blocker, loaded google.com, clicked no, not interested, then re-enabled my ad blocker, from that point forward it stopped asking me. Until I did that, it did it every time I went to google.com. You might have to redo this if you clear your cookies.
Solution 3:
For Edge try this... Open Edge then click F12. Find the Emulation tab then under Mode open the drop down list named "User agent string". Select Google Chrome.