"Fixing" Toxicity.

This isn't covering toxicity that is generally reprehensible. This will not cover racism, sexism, and other related issues.
Those can't be fixed by Rare, only combated.
With that out of the way...

Sea of Thieves is an inherently PvPvE Game. Trying to boil it down to just PvE puts an amount of pressure on the PvE side which it simply cannot bear.
This will NOT be a suggestion to make Safer Seas the Default. I personally would rather have Safer Seas removed instead of that happening.

So what is a major driver of Toxicity anyways? Well from my experience (Both on the Aggressive and receiving side) it's imbalance in PvP.
I think most people have experienced this before. After completing a Mission or Event or whatever, you get approached by another ship.
In this moment, you have two options. Stay and fight, and risk losing everything, or Run, attempting to sell your items along the way.
Both options suck for one of the parties.

As someone not engaging in PvP, you have no reason to stay and fight. You can literally only lose, as most experienced PvP players will not carry loot for long.
Yes, you could take the supplies from them, but nothing that PvE can offer needs that level of supplies. So why WOULDN'T you run? There are no incentives to stay.

But Running sucks for the PvP players. It's boring for one, it has no strategy to counter it and it's just wasting time that could be spent fighting instead.
And yeah "Just play Hourglass" if you want PvP, right? But that just isn't the same, and Rare even acknowledged that the PvP part of High Seas is the main aspect of the game.
So the only real way to get into altercations consistently is to get the jump on the other ship, which in return sucks for them as nobody likes getting Blown up out of nowhere.

It's obvious how this is the perfect ground for toxicity. One Side has to watch a 30 minute mission be made pointless in a few minutes without being able to do anything about it,
while the other side is basically begging for a fight that they will never get if the other crew is even mildly competent.

And Both sides are entirely justified to feel awful about it!

So what to do about this?

1. Give an incentive to stay and fight instead of running. This could be guaranteed rewards or renown boost for beating a ship or something similar. Commendations, Cosmetics, Literally anything.

2. Alternatively or additionally, Nerf Running. Rare already experimented with that with the Skull of Siren Sorrow. I suggest we give a weaker version of that to Every Item of Loot.
   It's pretty odd how you can carry literally tons of gold on the ship yet not be slowed down one bit. If having large piles of Loot would slow you down enough for other ships to catch up to you,
   Not only would there be an incentive to stay and fight, but also to plan your voyages better, to make selling runs as short as possible.

3. A Skeleton Watcher maybe? Back when I played with Friends a lot, we would always leave a watcher at the ship to look out for incoming threats. This worked pretty well, but of course it sucks for the one left behind. Now with the AI skellies and ghosts, why can't we find or buy a Skeleton crewman who's only job is to sit in the crows nest and bang a Drum whenever he spots a ship on the horizon? Basically something that makes it easier to avoid getting jumped out of nowhere. It shouldn't be mandatory, and you should still get punished for ignoring the warning, but a little bit of help can go a long way in levelling the playing field. It would also help out Solo Sloopers quite a bit.

4. Cannons at the front and Back (that aren't the cannon of Rage). If you want to you can even make these cannons refuse the regular cannonballs and only accept Cursed Balls and Chain Shots. Just literally anything you can do when running (besides boarding backwards). This helps both to Combat running and to defend while running.

Or you can do none of that. These are just ideas. But the problem still remains.
As long as there is no reason to stay and fight, people will run.
As long as people are running, the Attackers will attempt to sink them without allowing a fight.
And both of these make people understandably mad.