Praise be to Allah

Firstly:

“Carrageen is also a polysaccharide and is produced from red algae. It is primarily used in the food industry as a gelling agent, for example in a number of slimming and light products or numerous other goods.

One example here are meat products that are made to gel by the carrageen.
Alternatively, carrageen can also be used as a thickening agent. Here, this algae product is used in jams, baby food, dairy products and desserts.”

http://www.birkamidon.com/products/carrageen/

There is nothing wrong with consuming items made from algae, because the basic principle concerning that which is extracted from the sea, plant material or otherwise, is that it is permissible, so long as it is not harmful.

Allah, may He be exalted, says (interpretation of the meaning):

“Lawful to you is game from the sea and its food as provision for you”

[al-Maa’idah 5:96].

Al-Qurtubi (may Allah have mercy on him) said:

“and its food” – this refers to any kind of food, and it may refer to a specific nutrient or health requirement, such as water on its own, wheat on its own, dates on their own, yoghurt on its own; it may also refer to sleep, as mentioned above.

Here it refers to what the sea casts up and what floats on its surface. Ad-Daaraqutni narrated from Ibn ‘Abbaas, concerning the verse “Lawful to you is game from the sea and its food as provision for you and the travelers” [al-Maa’idah 5:96], that “its game” refers to what is caught and “its food” refers to what the sea casts out.

A similar report was narrated from Abu Hurayrah, and this is also the view of many of the Sahaabah and Taabi‘een.

It was narrated from Ibn ‘Abbaas that “its food” is what is found dead of its animals.

It was also narrated from him that he said: “its food” is that which becomes salty and is thus preserved. A number of other scholars said the same.

Some scholars said: “its food” is its salt, which is extracted from its water, and everything else that is in it, plant matter or otherwise.

End quote from Tafseer al-Qurtubi (6/318).

Secondly:

If the production of this substance and the crystallisation thereof is done by means of alcohol, but no trace of alcohol is left in it, in the sense that if a person were to consume a large amount of this substance, he would not become intoxicated, then this is overlooked, because it is a small amount that is absorbed completely.

In Tawsiyaat Nadwah ar-Ru’yah al-Islamiyyah li Ba‘d al-Mashaakil at-Tibbiyyah, it says the following:

Additives in food and medicines that come from an impure (najis) or unlawful (haraam) source become permissible substances, according to Islamic teachings, in one of two ways:

1. Transformation (istihaalah)

What is meant by transformation, in fiqhi terminology, is changing the nature of the substance that is impure or unlawful to consume, and turning it into another substance that is different from the original substance in name, characteristics and qualities…

2. Absorption (istihlaak)

This is done by mixing the unlawful or impure substance with another that is pure (taahir) and lawful (halaal), and of a greater quantity, so that it takes away from it the quality of impurity and unlawfulness, as the characteristics of taste, colour and smell of the lesser substance disappear as it is absorbed into the substance that is greater in quantity, and the ruling is connected to that which is greater in quantity and dominant.

An example of that is as follows:

Additives that are soluble in alcohol, which are used in very small amounts in foods and medicines, such as colourings, preservatives, emulsifiers and antioxidants. End quote.

In Fataawa al-Majlis al-Urubbi li’l-Ifta’ wa’l-Buhooth (fatwa no. 34) it says:

In the list of ingredients of some foods there appears the letter E followed by a number. It is said that this means that it contains a substance manufactured from pork fat or pig bones. If that is proven, what is the Islamic ruling on those foods?

Answer:

What is referred to by the letter E followed by a number are additives of which there are more than 350. They are either preservatives, colourings, flavour enhancers, sweeteners, or other things.

They are divided, according to their origins, into four categories:

1.  Ingredients of an artificial chemical origin

2.  Ingredients of plant origin

3.  Ingredients of animal origin

4.  Ingredients that are dissolved in alcohol

…

With regard to the fourth category, in most cases this refers to colourings, which are usually used in very small quantities, so that they are absorbed into the final products, and this is overlooked.

End quote. From Fiqh an-Nawaazil by Dr Muhammad al-Jeezaani (4/263-267).

Based on that, there is nothing wrong with consuming carrageen, if it is in accordance with what we have explained above, and no harm will result from that.

And Allah knows best.