I usually render grassroots as popular (and vice versa), but sometimes as 'de base.' I've posted before about trabajo de base, and organización de base. An exception is comunidad de base (in the liberation theology tradition), where instead of grassroots I would use organized community. For grassroots diplomacy (people to people work, like delegations and exchanges) you could use de base too, but I heard this desde abajo rendition from Maguemati Wabgou and I love it. He used it on a panel entitled Geografías afrodescendientes y diálogos con las Áfricas which was part of the section Diálogos improbables: movilidades y disputas de saberes en el
Segundo
Encuentro Latinoamericano de Movimientos Socioespaciales y Socioterritoriales.