Can you eat a dairy product that doesnt have a Hashgacha if it is vegetarian and certified as such by competent public vegetarian entity.
Just because the ingredients don’t contain animal products doesn’t automatically make them kosher. The machinery that the product is made on, may have been used to do a trief run before this product was made. There can be issues of chalav akum, cheeses can be made inside treif animals and got their taste. There can be bishul akum issues, or an issue of insect infestation, stam yanam. chametz after Pesach, or Chodosh. Now a number of these topics will not apply to most products, and I only mean to bring out the point that there can be other issues aside from trief and basar bchalav. Besides, even a public vegetarian entity, may have certain guidelines of ow much animal products and derivatives they do allow. Therefore, this is not enough to permit eating product without a hechsher, even though the product doesn’t have any known animal derivities inside it.