I would like to build a social navigator. Any suggestions? I think the Navis Scion is a good choice. But how to dodge the negative mutations that give you minus Fellowship? Are there any items that can help?

Aside from never learning more navigator powers? There's always Dark Pacts, but we don't talk about those.

Be from a high house that grants you bonuses to resist mutation, and then flat out do not care if people find you gross and disgusting (they will and you are). There are some items that grant you bonuses to social tests, like Mefonte's Orthodoxy from Core 145, the Lightbringer Torch from Stars of Inequity 95, and the Maxims of Marquette from Faith and Coin 97

The Navigator in my campaign is an arrogant prick who made sure to max out his Toughness before advancing his powers to avoid this, and he still used his creepy mutations to fold all his joints in seemingly impossible ways so that he could hide inside a cabinet to avoid an Arco-Flagellant that was hunting him.

You want the Navis Scion from into the storm, IIRC.

The Navi in my long-running RT campaign was exactly that. High house, Navis Scion. Total socialite. Worked reall well, TBH. Though it did help that she avoided all the gross mutations.

Shrouded houses give bonuses to social skills in more situations, not only with officials and in formal settings. But they mutate, yes.

I'm not going to sit here and type up my whole diatribe about how this is something you would want as a character, but not always something your well-RPed character would, because I specifically built one, too, and because everyone has their own preferences, but I will say most Navigators don't try to dodge their mutations, and they benefit because most people who they deal with HAVE to deal with them, no matter how they look, smell, or whatever.

While it is expensive in XP, I guess I'd say sink the points into Toughness advances, as I believe the check to resist mutations, either by growing your powers, or the other excuses that then auto-shift to your mutation table, are Toughness-based. Otherwise, chat with your GM ahead of time, to get their input on cybernetics fixing some mutations, as I know the thread I did type said block of ungh! into was also visited by people proposing just lopping off "defective" bits, and replacing them, unless you have Strange Vitality; we argued as to how that and cybernetics might interact. Mine has ridiculous Fellowship, decent Toughness (both were a bit spendy), Navis Scion, and two mutations: Strange Vitality and Claws. She is very self-conscious about her hands, especially as she is as much a Firefly Ambassador as she is a Navigator, and so she has best-quality padded gloves that cover her arms to the elbows, and never removes them in front of anyone. Her warp eye is hidden behind a fancy headpiece with an occulus in it. She's resisted mutation since. it can be hard; it's SUPPOSED to be, I suppose, to avoid further mutations, but again, if you decide your character actually wants to, rather than you would just rather, certain applications of just money, and maybe some cybernetics, can stave off a lot of this, and paying out the wazoo into Toughness can help, too.

Best of luck.

Navis Scion is an awesome class to play! I highly recommend you also double as the ships Seneschal in name at least. Makes for great opportunities for roleplaying!