Thai curry recipes often use a lot, and the flavour is distinctive.
You'll need to experiment.
Your idea of cashews is a good place to start.
What I've often used in Indian curries is ground almonds (almond flour would be better but I can't get it easily).
They have some thickening power and quite a suitable taste.
You could also try cooking with nut milk - I've only done this a couple of times because it's not something I normally have, but recently used some almond milk in a sauce with lentils etc.
It ended up with a fairly creamy texture.
This was a brand marketed for cooking and a little thicker than I've come across before As an aside, I hope you've had medical confirmation of the allergy
- it's not exactly unknown for these things to be deceptive.
cooking.stackexchange.com/users/20413/Chris H
Substitutes have been mentioned already, but how about going the other way?
There are more curries without coconut than there are with it.
Many many curries use an onion base for thickness; coconut is a Southern Indian/Sri Lankan twist on what is a continent-full of cuisine.
Look down the even just the standard sauces of any take-away menu...
Bhuna Madras Vindaloo Jalfrezi Rogon Josh Dopiaza Pathia Dansak
The list goes on... & not a coconut in sight.
Or for more variety, how about Ethiopian Wat, or a Moroccan Tagine?
For Thai, have a look at a Jungle Curry - again, no coconut.
cooking.stackexchange.com/users/42066/Tetsujin
I don't know much about Thai curries but there are plenty of Indian curries that are broadly similar to coconut-based ones but with sauces made with cashews and other nuts.
Typically, you'd want to soak the nuts for a few hours and then blitz them into a puree, or just use a nut butter because life's too short.
Indeed, there are many Indian curries that don't use coconut or any other nut.
Coconut is basically a south-Indian thing and being allergic to coconut doesn't stop you eating Indian food, just like being intolerant of pasta wouldn't stop you eating European food.
I suggest you get yourself a good Indian recipe book.
I'm a huge fan of Camellia Panjabi's 50 Great Curries of India , because it has a pretty long introductory section that explains what all the different ingredients are for, which is really helpful when, for example, you can't eat coconut
but you want to make something similar.
cooking.stackexchange.com/users/24117/David Richerby
We cooked a lot of vegan at home for some time and often used soy cream as substitution for sauces that demanded cream.
It has a unique taste, but I do not find it unpleasant.
It has about the same thickness as coconut
and I think the taste is also quite fitting for curries.
As others mentioned, some almonds or cashews could enhance the experience.
In Germany, I usually find this soy cream in the vegan/non-dairy aisle next to the other soy products.
cooking.stackexchange.com/users/55819/Ian
As we do not know exactly what you allergic to (you said coconut but it could be coconut milk, an additive in the milk or coconut in general), I will make some extra suggestions: 1)
You might be able to try adding natural coconut flavouring to the already mentioned nut milks (cashew or almond).
This might tip the scales in making an Indian style almond based curry taste like a Thai coconut milk based curry.
2)
If you are allergic to everything
coconut
then you could try Imitation Coconut Extract which shouldn't contain any coconut.
Again, this might tip the balance on the other nut-based milks.
3)
You could try adding gorse flower extract.
I have never tried it
but I do know from roaming the coastlines and moorland of Devon , that gorse smells a lot like coconut.
It is edible , is common year-round and according to eatweed.com , has a subtle coconutty taste.
I see no reason this could not be added to a curry to infuse further coconut tones.
Finally, if you are allergic to all coconut, here is a quick and helpful guide to replacing all coconut ingredients .
cooking.stackexchange.com/users/40366/josh
I can only speak to south indian curries.
I don't have a substitute for coconut but you can certainly make a great curry without dairy or coconut added to the mix.
You can make a delicious sauce from just water and emulsified fats combining with your choice of spice meats and veg.
I have only experience with meat based dishes
so this may not work out for any vegetarian attempts.
Meat releases fat and water when covered and heated.
After I sauté the veg (typically ginger, garlic, onion), I add the meat which has been marinating in spices and oil (or just dry rubbed with spices).
I cover the pot and keep the heat on high for a few minutes until I see water appear at the bottom of the dish.
Then I reduce the heat to med low and leave it covered for 30 mins or so.
Over time more water and fat is released and the meat should be practically swimming.
From there I simmer uncovered for as long as I need to thicken the mixture.
This also concentrates the flavors.
Chicken stock also can be added.
Even plain water.
You'll also get water from watery veg like tomatoes.
I'm pretty sure you could add kool aid if you wanted to.
Most of the flavor comes from the spices and chillis.
cooking.stackexchange.com/users/42704/jmathew
North indian and Pakistani food uses a combination of onions, tomatoes and ginger garlic paste to form the curry base.
First you fry some finely chopped onions until they turn golden brown, then add about a tablespoon of ginger garlic paste, finely chopped tomatoes and the spice powders (chilli powder, turmeric etc.).
You let that cook stirring from time to time until the tomatoes turn into a slurry.
That's your curry base!
There are many videos on youtube that show you how to make this in case you want to see it in more detail.
It's also possible to substitute yoghurt (curd) for tomatoes.
cooking.stackexchange.com/users/73532/Abdussamad
I'm allergic to coconut - this is a new allergy, so I really miss Thai and Indian curry! I also have issues with dairy.   Would it work to use roasted cauliflower puree as a curry base instead of coconut? Maybe with a little raw cashews pureed to add creaminess.  Are there other options to satiate my dreams of curry without coconut or dairy milk?
What are substitutions for coconut in curry?
cooking.stackexchange.com
<substitutions><curry><coconut>
cooking.stackexchange.com/questions/96917
cooking.stackexchange.com/users/73500/Jessica
Many Indian and Thai curries do not use coconut at all, so you could try some of those recipies. Alternatively, cashew, almond, soy and some other options can be used, either soaked or as milk or butter. You could also try gorse flower extract. Nuts are considered a good substitute for coconut in curry. It may also be worth trying gorse flower extract and soy cream. However, there is a wide range of recipe for curry without coconut, so no substitute is needed.
Coconut can be replaced by other nuts such as cashews and almonds in curry. Other options are soy cream and gorse flower extract. Many curries do not use coconut so there are numerous recipes available.