Workaround by valhallasw:
When typing in the "projects" field in the "edit task" or "edit search" view, phabricator offers up to 5 suggestions/completions. But sometimes, the exact match for what I just typed is not included in this list. This makes it impossible for me to enter these projects anywhere (for me, this happens for "wikidata" - I see "wikidata.org" etc, but not "wikidata"). Interestingly, these suggestions look different for other users (with the same input, they do get "wikidata", though it's only in the 4th slot), so it seems the ranking in the suggester is user-specific (projects that I am a member of get boosted, or some such).
In any case: exact matches should always win. If I enter a full name and hit enter, this should always work if a project by this name exists.
I'm setting this to "high" since it makes it pretty much impossible for me to work with phab.
PS: I suppose the same issue exists for all fields that use the suggester/tag logic, but I did not run into any problems with other fields yet.