I write a lot of non-human cultures in my world. In my case, I have taken to exploring what's the same between the cultures and thought processes rather than what is different.
Generally, all living creatures want to live, and they want to reproduce.
Those are the basics. You can build from there.
Living = taking all necessary actions to assure your biological survival. This can differ depending on the biological needs of your races. But, it does essentially boil down to nourishment (whatever form that takes) and security (protection from whatever might be considered harmful to them. In human terms, this usually means shelter.)
Reproduction is a trickier subject, because there are 2 primary reproduction strategies. The R reproductive strategy means just producing offspring in as large of numbers as possible, and not worrying about how they grow up. Rabbits are the typical example of an R reproductive strategy, but the goblins from goblin slayer's world would be so heavily in the R direction that they are actually further in that direction than rabbits. However, the absolute most extreme example would be spiders and most species of fish, which just create hundreds of offspring and then leave them to fend for themselves. Spiders even take it to the extreme of viewing their own offspring as a potential food source, actually killing and eating them if they don't run away fast enough. That probably places spiders at the #1 most extreme level of the R reproductive strategy, literally producing hundreds and then very literally not caring one bit whether they live or die to the extent of killing them themselves with no parental instinct at all.
The other reproductive strategy is called the K reproductive strategy. This describes a quality over quantity approach toward raising offspring. In a K strategy, there is a lot of parental instinct, and they will dedicate a great deal of resources toward raising children. Humans are often thought of to be a middle point between the two because we see humans varying more toward one direction than the other, but actually humans are very heavily in the K direction in terms of reproductive strategies and the differences in behavior you see are just natural variations in behavior.
I am sure, for instance, you can find spiders that will not consider their own offspring as food. So, that would be an extreme R species that is varying a little more in the K direction than is typical for their species. In that same vain, you have your dead-beat parents with irresponsible sexual practices among humans who are more R than the standard extreme K of the human species.
Anyway, the reason I say humans are an extreme K species is because of women experiencing menopaus. This is an evolutionary trait that is meant to facilitate grandparents aiding in the raising of their grandchildren. They stop having kids among the older generation, so they can help raise children 2 generations younger than themselves. This is a very extreme K reproductive behavior.
So, those are the base essentials that every race needs to have.
1. Filling the need for nourishment.
2. Filling the need for personal safety. If they are a communal species, then this extents to the entire community. (One point to note, self-sacrifice for the benefit of others is a behavior of a communal species.)
3. Filling the need for reproduction. You need to consider, however, whether this is more of an R reproductive species, or a K reproductive species.
Once you know those 3 foundational points that apply across any species, you can begin building their culture from there. Once you have built their culture, said culture will begin affecting their thought process.
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