Social Justice: Code word for wealth redistribution.
Usually when I see Social Justice, it is being used as a code word for identity politics. E.g. it is not socially just to use the term blacks. You should say African-Americans instead. Also see Social Justice Warriors. It is of course possible that you run in different circles than I do.
This would not generally be considered a dog whistle, as it doesn't hide one policy with another. I've never heard anyone say social justice, mean wealth distribution (or identity politics), and try to argue that social justice is not actually wealth distribution or identity politics.
Diversity might be considered a liberal dog whistle. As practiced, it often means setting different standards for one demographic than another. For example, Harvard excludes Asian applicants at a higher rate than black applicants. This is a dog whistle because it hides preferential treatment based on race behind a policy that claims to promote equal opportunity.
An example of what I would consider a liberal dog whistle is assault weapons. So-called "assault weapons" are semi-automatic rifles that look like the assault rifles used by the military. They are popular for the same reason that water guns that look like real guns are popular. They look dangerous. But in reality they are no more dangerous than other semi-automatic rifles with similar shooting characteristics.
By using the term "assault weapons", liberals imply that these are just as dangerous as military assault rifles. And you can see this in the rhetoric around them. They are described as designed for military use with no civilian purpose. This is of course hooey. No military in the world uses semi-automatic versions of fully automatic weapons. They may use semi-automatic rifles for things like sniping, where a single shot is sufficient.
The television show Supergirl had a recent episode, Not Kansas, where special large caliber rifles were available with bump stocks. However, assault rifles are not larger caliber than other rifles. In fact, they are generally smaller. Why? Well, let's consider a scene from the episode.
The villain is shooting one of these magic rifles at Guardian (an armored hero). The bullets are physically pushing Guardian backward even though he was braced against the shots. However, real guns don't work that way. If a bullet has sufficient momentum at impact to push a large man in armor back, then it must have had an even higher momentum when it was expelled from the rifle (air resistance reduces momentum as the bullet travels). Firing would also push the unbraced, unarmored shooter back. As Isaac Newton explained for every action there is an equal and opposite reaction.
An actual human being shooting a real fully automatic, large caliber rifle would fall over. This is why a weapon like the M2 Browning is mounted on a turret. The recoil in fully automatic mode would knock over a human being who tried to fire the thing. But that's okay, Supergirl is fantasy. They can have magic guns. The ironic thing is that they seemed to present both sides but did so in such an unrealistic way that it was obvious which side viewers should pick.
An assault rifle is generally rather small caliber for this reason, to allow real human beings to manage the recoil of a fully automatic weapon in continuous or burst fire. For example, the ubiquitous M-16 is a .224 or just slightly larger than a .22. The semi-automatic version, the AR-15, is the same caliber. Meanwhile, many hunting rifles will be a larger caliber, e.g. a .300 or .375. And handguns are often even larger, e.g. Dirty Harry's famous .44 Magnum. That's almost as big as the .50 M2 Browning.
Rifle cartridges are often longer than handgun cartridges, not a larger caliber. The length gives more speed out of the muzzle. That's part of why handguns can be larger caliber. They're shorter and slower, so their momentum or recoil is lower than it otherwise would be.
Anyway, back to dog whistles. I would consider an "assault weapon ban" to be a liberal dog whistle because it makes no policy sense to single out "assault weapons" while leaving other weapons that are at least as dangerous if not more. But in many districts politicians can't say that they want to ban all guns. So they instead talk about "assault weapons" as being easy to demonize. Meanwhile, most homicides and suicides are committed with handguns, which are easier to use and to carry concealed.
Some gun-rights activists believe that this is intended as a policy of harassment. Because long rifles are commonly owned but rarely used in crimes, a policy restricting them doesn't make much sense from a crime reduction standpoint. However, it is annoying to gun owners and reduces their enjoyment in collecting guns. After all, semi-automatic versions of assault rifles are probably as close as most gun owners will get to owning an assault rifle. If some of those people don't bother to own guns at all, then they are less likely to resist other gun restrictions.
The phrase "Assault weapon ban" is a dog whistle because it hides one policy (eliminating all private ownership of firearms) with another policy (restricting one class of firearm).
Another issue with the term dog whistle is that it is usually used as an accusation. One person says about another person, "When you say [dog whistle], you are signalling that you support [some bad thing]. But you don't come right out and say it, even though you believe it." Two things:
The person making the accusation doesn't actually know if the person being accused really thinks that way. That is an assumption.
For example, many liberals say that they don't want to take away hunters' guns; they really just care about the immediate policy. That may seem unlikely, but it is not impossible. In fact, the whole purpose of a dog whistle is that for some people, the dog whistle is acceptable but the alleged policy is not. If that weren't true, there'd be no reason to use the dog whistle over the policy.
There must be at least some people who agree with the literal policy without supporting the hidden agenda. Any given individual may be one of those people.
This then becomes a form of virtue signalling. Liberals accuse conservatives of dog whistles. Conservatives accuse liberals of virtue signalling. Saying that black lives matter is virtual signalling. What many conservatives hear is that black lives are more important than white lives. Saying that all lives matter is a dog whistle response. What many liberals hear is that white lives are more important than black lives. In both cases, they infer something different than what was actually said.
Virtue signalling is also stigmatized as saying something to avoid doing something. For example, Democrats say in their platform that they are against illegal immigration. But when it comes to actually doing something about it, they won't support any of the policies to reduce illegal immigration.
A dog whistle is something of the reverse. It's supposedly saying a relatively innocuous thing so as to attract people that believe something else. The problem with a dog whistle is that it may turn into the policy and then be expanded.