[Affected versions]:

• Windows 10 x64
• Ubuntu 18.04 x64
• macOS 10.13

[Affected platforms]:

• 60.5.0esr (20190124141046)
• 65.0 (20190124174741)
• 66.0a1 (20190122232941)

[Steps to reproduce]:
Make sure to have a normal and a private window opened

1. Go to about:preferences#search
2. Go to One-click search engine section and set a keyword for any desired search engine
3. Go to the private window and set the same keyword for a different search engine
4. Refresh both windows
5. Inside either window, click on any of the duplicate keyword and press Enter (don’t change the keyword)

[Expected result]:

• The same keyword can't be set on a different search engine.

[Actual result]:

• [4] Both search engines have the same keyword set.
• [5] Duplicate keyword warning message pop up shows up, any action inside the window triggers the pop up appearance (see screencast); changing or deleting the keyword fixes the issue.

[Regression range]:

• This doesn't seem to be a regression, I could see this behavior way back to Fx 40.0a1.

[Additional Notes]:

• When performing a search using the set keyword, the search engine used is the last one, on which the changes were applied, regardless if it was set from normal or private window.
• Multiple duplicates can be set corresponding with the number of private windows opened.