Is ice cream made with seaweed?

Yes, it can be:

Agar is a gelatinous substance derived from red algae (red seaweed).

Historically and in a modern context, it is chiefly used as an ingredient in desserts throughout Asia and also in the past century has found extensive use as a solid substrate to contain culture medium for microbiological work.

The gelling agent is an unbranched polysaccharide obtained from the cell walls of some species of red algae (red seaweed).

Agar can be used as a laxative, a vegetarian Gelatin substitute, a thickener for soups, in jellies, ice cream and other desserts, as a clarifying agent in brewing, and for paper sizing fabrics.

Chemically, agar is a polymer made up of subunits of the sugar galactose. Agar polysaccharides serve as the primary structural support for the algae's cell walls.

Answer: There are many differerent gums you can use to make ice-cream, you can make it without! So it really depends on the brand. Agar can come from Gelidium amansil (it shows up as E406 in ice cream). Chondrus crispus is somtimes used for Carrageenan (listed as E407 in your ice cream) You can get them from other species too; though generally red seaweeds.