Six main factors are at work.
First, in most states, political boundary lines are fairly arbitrary, with suburbs and central cities being in different jurisdictions. In Hawaii, in contrast, county lines largely correspond to island boundaries, so counties include all central cities, suburbs, and rural areas on that island.
You see something similar in Columbus, Ohio, which is a city that integrated most of its suburbs into a single political entity, making it seem more conservative that it would if it had a smaller central city and more of its fringe neighborhoods were in their own separate political jurisdictions.
Second, Hawaii is also a state with a heavy military and ex-military presence and that presence is concentrated in Honolulu county. The military and ex-military voters are more conservative than Hawaii voters as a whole and more culturally and religiously similar to rural white Christians in the U.S. and their presence influences the politics of Honolulu somewhat.
Third, Honolulu is also home to the most affluent Asian Americans in the state, for the most part, who are most prone to vote Republican rather than Democratic, among Asian Americans.
Fourth, Hawaii is heavily non-white (mostly Native Hawaiian, Pacific Islander, Asian and mixed race from partially those origins), and has few rural white Evangelical Christians, in contrast to most U.S. states.
As of the last American Community Survey of the U.S. Census Bureau prior to the U.S. Census for 2020 which hasn't been released yet to this level of detail, the racial composition of Hawaii was:
Two or more races: 23.89%
Native Hawaiian or Pacific Islander: 10.06%
Black or African American: 1.83%
Other race: 1.23%
Native American: 0.26%
Somewhat older data (from 2014) reveals the general trend by county in Hawaii in terms of racial makeup:
What did the racial composition of our population look like on July 1,
Asians (alone or in combination) accounted for 56.2% of the state total population. Honolulu County had the largest percentage of
Asian (alone or in combination with other races) population at
60.2%, followed by Kauai County at 50.8%, Maui County at 47.1%, and Hawaii County at 45.0%.
Native Hawaiians and Other Pacific Islanders (alone or in combination) accounted for 26.0% of Hawaii’s total population. Hawaii
County had the largest share of Native Hawaiians and Other Pacific
Islanders at 34.4%, followed by Maui County at 27.7%, Kauai County at
25.7%, and Honolulu County at 24.1%.
White (alone or in combination) accounted for 43.6% of the state total
population. Within the state, Hawaii County ranked the first in
terms of shares of White population. 56.3% of the total population on
the Island of Hawaii was White alone or in combination with other
races on July 1, 2014. Maui County had 52.2% of the White population
and ranked the second, followed by Kauai County at 51.8%, and then
Honolulu County at 39.1%.
Honolulu County has the lowest share of native Hawaiians who are the most liberal leaning significant racial/ethnic group in Hawaii.
Also, about 43% of whites in Hawaii as a whole are mixed race Hawaiians (a percentage unprecedented in any other U.S. state), and this is probably higher outside Honolulu, than in Honolulu. But, politically, in the U.S., mixed race whites tend to identify as Democrats rather than as Republicans politically.
Hawaii is also a state with a high proportion (36%) of residents who are not religious or are affiliated with a non-Christian faith, both groups that lean left politically:
Unlike most of the U.S., rural areas in Hawaii are heavily non-white and the whites who live there are also mostly not Evangelical Christian, unlike most rural areas in the mainland U.S. which are mostly white and conservative Christian. Many Evangelical Christians in Hawaii are not white and, non-white Evangelical Christians tend to be much more liberal than white Evangelical Christians politically.
Fifth, historically Hawaii's farming and fishing industries were carried out mostly with local Native Hawaiian labor and imported non-slave Asian labor, not with African slaves or European migrants, and so the cultural and legal norms developed in response to slavery and European migration that are at the root of a lot of U.S. political culture didn't emerge in Hawaii in the same way. So, culturally, rural Hawaii is very different than rural areas in the mainland U.S. and is more left leaning as a result.
Rural Hawaii is somewhat comparable to rural New England in the sense that both share a very different cultural and political history from that of the bulk of rural areas in the mainland U.S.
A closely related factor is that Hawaii was not part of the U.S. at the time that the formative primary left-right political divisions in the mainland U.S. emerged (i.e. before, during and immediately after the U.S. Civil War). So, it doesn't share the political history of similarly situated parts of the mainland U.S.
Hawaii also largely did not participate in the manufacturing economy and its subsequent Rust Belt collapse that was politically formative in mainland partisan politics, or in mass European migration in the 19th and early 20th centuries which was also politically formative. Also, as a result, Hawaii did not participate in the "Great Migration" of black farmer workers to major industrial Northern cities in the mainland.
This has played into recent political history, because in many Northern states the Republican party base has recently seen a surge of supporters who are blue collar workers who are (or had parents who were) part of the manufacturing industry who grew disaffected with Democrats and unions as those industries collapsed. They turned instead to the wing of the Republican Party culminating in President Trump's wing of the GOP. Since Hawaii outside of Honolulu has few people who were part of this demographic, it hasn't seen the shift to the political right of the mainland Rust Belt, while Honolulu has far more people who are part of this demographic.
In short, Hawaii's formative political history was largely divorced from that of the mainland, so the generalizations arising from that history that work for the mainland don't work as well in Hawaii.
Sixth, rural Hawaii defined as outside Honolulu is partially an agricultural economy, but is more so a tourism driven economy. While places with exclusively agricultural economies tend to be conservative politically, places with heavily tourism based economies tend to be more liberal.
For example, in Colorado, the tourism driven mountain towns tend to be liberal, while the agriculture driven Front Range and Western Slope tend to be more conservative.
Again, the anomaly here is that rural Hawaii is liberal, not that its central city is liberal (which is expected).