Ok, so the rep system for mnavy has gotten an overhaul, after many years of nobody really knowing how in the world to get rep, Tarken has updated everything. With the old system, you got rep assigned to you when you summoned your ship. Anything that you did to try to gain rep got tallied, but not awarded until after you summoned your ship, after the next reboot. It was kind of a cumbersome system, also it was put into place before the current continents were, and it wasn't designed much for all the sailing we have to do nowadays. So, here is the newspost from Tarken, talking about the new rep system:

Group: guilds.sailor (#417/417)
From: Tarken (Lvl: 145 [Wizard] Age: 3y, 5d, 14h, 53min and 3s)
Subject: New Merchant Navy System
Date: Wed Jul 04 04:41:15 2012
Rating: 0 Votes: 0

The time is finally here, yes indeed it is. The Merchant Navy system was long
overdue for a complete overhaul. The way it was previously coded, most
reputation was based on a series of (generally) one-time investments and
relatively little expectations regarding activity whatsoever. Well, this has
been changed.

Life in the Merchant Marines is rarely dull for those who know what they are
doing. Constantly seeking out the best bargain requires a great deal of travel
across the Realms, locating those with a need for goods and matching them up
with those who have a surplus. Money is what makes the mercantile world go
round; accordingly the merchants who make the most money inspire the greatest
'loyalty' in their crew, and achieve the greatest degree of fame. A reputable
Merchant Marine travels far, hauling cargo and passengers across the realms,
and offloading large amounts of goods across the various continents and islands
of the realms. Only the hardest working Merchant Marine can quickly achieve the
highest levels of  reputation. This doesn't mean that an old and hardened
sailor won't be known for his travels either.

Something quite different than usual, the exact activity levels required in
order to gain reputation are not exact, as they are now as dynamic as the
population which they govern, rising and falling with the tides of the economy
and those who choose to partake in it.

You may choose to start earning reputation now with a 'real' quit-out, or wait
until reboot.

Furthermore, there will be additional opportunities in the future to earn
pseudo-unlimited rep (much like the combat-based alignments), though I have yet
to establish any timeline on completing these projects, albeit they have been
discussed for implementation.

Sadly, simply summoning your ship will not be enough to gain reputation anymore
(at least at any useful rate, if at all...we'll see.).

Happy sailing,

-- Lord Tarken Aurelius, the Magus

As you can see from the post, you have to do more 'merchanty' type things to gain rep in the new system. Here are some things that I have noticed that give rep with the new system. Tarken has said that there is a cap on the amount of rep you can gain as mnavy per day, unlike the combat-oriented alignments of the sailor guild, but thats because honestly, its pretty safe as mnavy, as long as you take sensible precautions in your ship handling, paths, where you park, etc. So, the things I have noticed are....

• Sailing around solo, with passengers, with cargo gives some small rep. I have also noticed that the rep gain tends to drastically slow down with just sailing. Meaning that the first couple points come pretty quick, then takes ALOT more sailing to get more.
• Carrying loot from one continent to another in your ship's holds and then selling it via the 'manifest' command gives appreciable rep. It seems that the amount sold needs to increase the more stuff is sold throughout the day. Which sucks for those who can't get on right at boot and sell stuff.

This was verified by Tarken himself on mnavy channel:

Tarken <mnavy>: Reputation possibilitieis include (so far): sailing, sailing with passengers, transporting cargo, and manifest sales.

So, from what I have seen, it seems that you have to have a more mercantile outlook on life to gain rep in mnavy now. One thing I can see people doing is more runs to sell items, but switching continents to do their selling, to gain rep. Anyway, these are a few of the things that I have seen for the short while I have messed with the new mnavy rep system.