If you include Macclesfield as a conference side then I’d say you have to class Chester as the same.
Chester being my local side for the last 10 years, I have to say that their fans deserve to have non league football, they aren’t the nicest bunch of fans and are very entitled.
Macclesfield have played in the football league for a total of 17 seasons (having been founded in 1874)
Chester are not quite as old (founded 1885) but played in the football league for 74 seasons.
Think that's why old-timers (my age upwards!) will think of Chester as a football league club, but not Macc.
Also while I'm at it - Walsall should be in the all-time 3rd tier league. They've spent the most seasons (75!) of any club at that level, and it's not particularly close.