STR:

1. Go to Options ( about:preferences )
2. Go to "Privacy & Security" tab ( about:preferences#privacy )
3. Under "Address Bar" section at "When using the address bar, suggest" disable all preferences ( "Browsing history", "Bookmarks", "Open tabs" )
4. Restart Firefox (to make sure that these settings will be used)
5. Press only "^" or "*" symbol in Address Bar
   and see that Firefox Address Bar still suggests some bookmarks

:Virtual, could you try to find a regression range in using for example mozregression?

Updated STR:

1. Go to Options ( about:preferences )
2. Go to "Search" tab ( about:preferences#search )
3. Under "Default Search Engine" section disable all preferences ( "Provide search suggestions", "show search suggestions in address bar results", "Show search suggestions ahead of browsing history in address bar results" )
4. Go to "Privacy & Security" tab ( about:preferences#privacy )
5. Under "Address Bar" section at "When using the address bar, suggest" disable all preferences ( "Browsing history", "Bookmarks", "Open tabs" )
6. Restart Firefox (to make sure that these settings will be used)
7. Press only "^" or "*" symbol in Address Bar
   and see that Firefox Address Bar still suggests some bookmarks

It's not reproducible in Mozilla Firefox ESR 52.9.0 (64-bit).

(In reply to Release mgmt bot [:sylvestre / :calixte] from comment #1)

:Virtual, could you try to find a regression range in using for example
mozregression?

Sure, working on it.

Afaict, we just made that change in bug 1550025, that was marked as a regression, and the current behavior makes sense anyway.

Just to clarify, using a restriction token is a clear indication the user wants to restrict results to the given type, and because of that it can bypass the pref. Otherwise the user would get no result. Afaict this regressed with Quantum Bar and was fixed in bug 1550025

(In reply to Marco Bonardo [::mak] from comment #5)

Afaict, we just made that change in bug 1550025, that was marked as a
regression, and the current behavior makes sense anyway.

Ahhh, unfortunately, too bad, as this kinda annoy me, especially when I'm using address bar as calculator and it spams me things I don't want to see, as I especially disabled them in Options.
It would make sense for me when I would like to search for only 1 of 2 or 3 selected search suggestion items, but when I don't want any, it's kinda illogical for me to show these suggestions.
Can't they be disabled when user disable all search suggestion items
and enabled when at least 1 (logical will be 2, but let's live with consensus for both sides) suggestion is enabled?

(In reply to Marco Bonardo [::mak] from comment #6)

Just to clarify, using a restriction token is a clear indication the user
wants to restrict results to the given type, and because of that it can
bypass the pref. Otherwise the user would get no result. Afaict this
regressed with Quantum Bar and was fixed in bug 1550025

Are there any more restriction tokens, than these 3 symbols: "%" "^" ""? As I found that also "%" shows items like "tabs to switch". "" shows probably bookmarks and "^" items from history. Is this correct?

(In reply to Virtual_ManPL [:Virtual] - (please needinfo? me - so I will see your comment/reply/question/etc.) from comment #7)

(In reply to Marco Bonardo [::mak] from comment #5)

Afaict, we just made that change in bug 1550025, that was marked as a
regression, and the current behavior makes sense anyway.

Ahhh, unfortunately, too bad, as this kinda annoy me, especially when I'm using address bar as calculator and it spams me things I don't want to see, as I especially disabled them in Options.
It would make sense for me when I would like to search for only 1 of 2 or 3 selected search suggestion items, but when I don't want any, it's kinda illogical for me to show these suggestions.
Can't they be disabled when user disable all search suggestion items
and enabled when at least 1 (logical will be 2, but let's live with consensus for both sides) suggestion is enabled?

This seems to add a surprising special case that may confuse users, that is what we prefer to avoid if possible. We'd better try to detect math operations, so when there is one of these symbols at the end but anything before it is a number or a math operator. Feel free to file a bug for this, it should be feasible I think.

(In reply to Marco Bonardo [::mak] from comment #6)

Just to clarify, using a restriction token is a clear indication the user
wants to restrict results to the given type, and because of that it can
bypass the pref. Otherwise the user would get no result. Afaict this
regressed with Quantum Bar and was fixed in bug 1550025

Are there any more restriction tokens, than these 3 symbols: "%" "^" ""? As I found that also "%" shows items like "tabs to switch". "" shows probably bookmarks and "^" items from history. Is this correct?

HISTORY: "^",
BOOKMARK: "*",
TAG: "+",
OPENPAGE: "%",
SEARCH: "?",
TITLE: "#",
URL: "$",

(In reply to Marco Bonardo [::mak] from comment #8)

(In reply to Virtual_ManPL [:Virtual] - (please needinfo? me - so I will see
your comment/reply/question/etc.) from comment #7)

(In reply to Marco Bonardo [::mak] from comment #5)

Afaict, we just made that change in bug 1550025, that was marked as a
regression, and the current behavior makes sense anyway.

Ahhh, unfortunately, too bad, as this kinda annoy me, especially when I'm using address bar as calculator and it spams me things I don't want to see, as I especially disabled them in Options.
It would make sense for me when I would like to search for only 1 of 2 or 3 selected search suggestion items, but when I don't want any, it's kinda illogical for me to show these suggestions.
Can't they be disabled when user disable all search suggestion items
and enabled when at least 1 (logical will be 2, but let's live with consensus for both sides) suggestion is enabled?

This seems to add a surprising special case that may confuse users, that is
what we prefer to avoid if possible. We'd better try to detect math
operations, so when there is one of these symbols at the end but anything
before it is a number or a math operator. Feel free to file a bug for this,
it should be feasible I think.

Let's better leave it alone in cases if someone has number or math operators as bookmark name, tag, etc.

(In reply to Marco Bonardo [::mak] from comment #8)

(In reply to Marco Bonardo [::mak] from comment #6)

Just to clarify, using a restriction token is a clear indication the user
wants to restrict results to the given type, and because of that it can
bypass the pref. Otherwise the user would get no result. Afaict this
regressed with Quantum Bar and was fixed in bug 1550025

Are there any more restriction tokens, than these 3 symbols: "%" "^" ""? As I found that also "%" shows items like "tabs to switch". "" shows probably bookmarks and "^" items from history. Is this correct?

HISTORY: "^",
BOOKMARK: "*",
TAG: "+",
OPENPAGE: "%",
SEARCH: "?",
TITLE: "#",
URL: "$",

Thank you very much for this!