Cooperation is far more common than any theory based on "cooperate with people like you" would predict
The trouble with this question is that is is a very big one which others have written whole books about so any summary will be incomplete and perhaps overly simple.
The most important conclusion is that cooperation between people goes far beyond what Haldane's numbers would predict and that reciprocal altruism base on consanguinity is not a good explanation for actual cooperation.
There are three key books that describe these ideas well: The Evolution of Cooperation by Robert Axelrod; The selfish Gene by Richard Dawkins; the Origins of Virtue by Matt Ridley (all links to latest editions on Amazon).
Haldane's numbers describe the mathematics of rational cooperation from the point of view of genetic success. It makes sense to display some degree of self sacrifice of an individual if their genes are preserved in the other relatives saved by the sacrifice. The theme of Dawkins' book is working out the implications of that view for biological behaviour. But rather too many people read the title and not the book and somehow never get to the penultimate chapter which (in my edition at least) is called Nice Guys Finish First. The chapter gives a summary of the work of Axelrod. Matt Ridley's book explores this theme in more detail.
What Axelrod did provides a powerful illustration that cooperation can be very effective for the individual and the group in ways that are far more significant for real behaviour than preferential behaviour to relatives. His basic idea was to create a computer model of individuals who would compete against each other in interactions with a Prisoner's Dilemma style payoff. The prisoner's dilemma is just about the simplest description of a two player game where the results are not trivial and where something like a real-world tradeoff between short and long term payoffs matters (the rational strategy in a single game is selfish, but if you know you will play repeatedly, you can do much better if you are not selfish). The beauty of the very simple game is how it captures the essence of some real interactions between people where the result is not zero-sum (i.e. the size of the pie can get bigger or smaller depending on how you play so there is more at stake than just what share you get).
Axelrod ran a simulation of many competing strategies for playing the game and ran competitions to see if experts in computer science, game theory and biology could develop effective strategies. The successful algorithms were allowed to grow in number; the less successful killed off in a long game with many rounds (in modern language he created a simulated ecosystem where individual bots with a particular strategy could recognise other bots they had interacted with before). The critical finding is what sort of strategy is successful in the long term: a selfish one, a greedy one, an altruistic one, a complex one and so on. Naively "nice" algorithms get exploited by nasty ones but if the population is all nasty, nasty ones don't do well either. Amazingly one of the simplest algorithms possible often comes out on top: tit-for-tat. It has the characteristics (as described by Dawkins) of
Tit for tat... is 'nice' meaning never the first to defect, and 'forgiving' meaning it has a short memory for past misdeeds. Tit for tat is also 'not envious' ...[which is] to be quite happy if the other player wins just as much money as you do.
There is a lot more detail which I highly recommend people to read, but the key point relevant to this question is just this: Axelrod's simulation demonstrates that cooperative behaviour can emerge from interacting individuals with no concept at all of kin selection (at least if you are playing a non zero-sum game).
Many creatures have the capability to cooperate for mutual benefit with their own species and with entirely different species (e.g. those small birds or fish that clean carnivores' teeth and never get eaten). Many species exhibit self-sacrificial behaviour with non-related individuals. Dawkins ends the description of this by describing mutualistic behaviour in Vampire bats where individuals who have had a good feed will regurgitate blood for unrelated bats who have not had a good feed. he ends the chapter with these words:
Vampires could form the vanguard of a comfortable new myth,a myth of sharing, mutualistic cooperation. They could herald the benignant idea that, even with selfish genes at the helm, nice guys can finish first.
The key point of all this is you don't need to be related to engage in and benefit from cooperative behaviour and that many of the actual examples of cooperation are not derived from the rules about how related we are, but from this, more powerful, drive for mutual benefit.
And, perhaps even more importantly for the original question, cooperation doesn't depend on whether the cooperating parties are similar. Otherwise different species couldn't develop symbiotic relationships. The critical issue driving cooperation is repeated interaction between people who recognise each other. This suggests that the correct prediction is that people will be more altruistic to other people they repeatedly interact with and those others may be completely unrelated.
