There are several main problems with vegetarian/vegan products.
1) The reliability of the vegan/halal certifying agency is questionable from a Halachik perspective. (That is, can they be trusted to check carefully? Can one rely on their word?)
2) Jewish law is extremely strict on the prohibition of eating bugs, which are common in vegetable products. (Though this is less of a problem in a paste or puree where the bug cannot possibly be whole).
3) The utensils used in the facility must also be Kosher (this is less of a problem in dairy and meat free facilities).
4)Additives (color, flavor, stabilizers) may be not kosher.
Additionally, many grape products are not kosher without certification due to the special prohibition of Yayin Nesech/Stam Yaynam.
All things considered, there is a decent chance that these pastes are Kosher. You can call up most major Kashrus agencies hotlines to find out.