Replacing cream and butter in a carrot casserole/pie

A mixture of almond milk and silken tofu (1:1) will yield an inexpensive half and half replacement, top with earth balance margarine as necessary. For baking, flax or Chia eggs or commercial egg replacer should fit the bill. If the baking time is not too long you can incorporate tapioca flour in slurry for a creamier texture and extra thickening, our just use a corn starch slurry.

Soy yogurt will add some creaminess and also a nice tangy flavor that goes very well with carrots. If you purchase whole fat coconut milk, you can skim the heavier cream layer off of the top and use that in place of the dairy cream as well.

Some food replacements for vegans are indeed rare and expensive. But for butter and dairy cream, there are easy replacements. Their unique texture and mouthfeel are due to the fact that they are emulsions of saturated fats. They are among the few naturally occurring such emulsions, but industry methods for creating emulsions are widespread, and manufacturers create these en masse with cheaper fats such as refined vegetable oil, and sell them for low prices in all supermarkets.

The substitute for butter is the well-known margarine. It is not perfect, and won't behave like butter in all settings, but it mixes very well with mashed vegetables, so it is very good for your use case. You can probably find several brands even in a small grocery store.

For the dairy cream, you can substitute plant-based "whipping cream". Depending on the legislation in your country, it can use the word for "cream" in its title and only note that it is a vegetable oil product in the fine print on the back, or will have a name different from "cream". The most popular such product here is the Unilever-manufactured Rama Cremefine (which comes in different variations, formulated specifically for cooking or whipping), but I guess this will vary by region. They are usually sold in the supermarket, stocked near the real dairy cream.

Just because a product is based on a plant oil, it doesn't mean it is always vegan. Sometimes producers add other ingredients, and you can't know if they are animal-derived. For example, Vitamin D is added to many margarines, and it is derived from wool fat, so vegans consider it an animal product. For each product, look for an assertion that it is vegan-suitable somewhere on the package, or contact the manufacturer. If the normal margarines and creams in your supermarket are not truly vegan, look at the organic brands, it seems they have a better chance of being vegan.