Actually not for the baggage, if you are on one ticket; if your HA segment is on the same ticket as the longer flights, DOT rules for baggage apply - meaning the most significant carrier's rules are applied. For an international trip, the MSC is the carrier operating the first TATL/TPAC segment. For domestic, it's the first carrier you fly on the entire ticket. Those rules are applied through the entire trip, outbound and return, since the DOT requires them not to change.

In other words, for any trip originating on the mainland with a Delta segment, Hawaiian will apply Delta's baggage policies; if you were booked in F on Delta, you should get free checked bags on checkin with HA in OGG on the return. Only if the HA segment is on the same ticket, of course.

I can confirm that on our HA-KE trip, the KE J rules were correctly applied and we didn't need to pay for baggage.

That leaves priority checkin. HA checkin at OGG was pretty chill for us, but we were admittedly flying at a weird time of day since we were heading west. I could see it getting more hectic around departure time for mainland connections.

(To be fair, I suspect HA would probably not collect bag fees if you were booked in F on their metal but connecting to an MSC who charges fees... but under the rules they would certainly be entitled to charge you.)