We studied the core bacterial communities of 19 sponge species from Nha Trang Bay (Central Vietnam), with particular emphasis on the contribution of planktonic seawater bacteria to the sponge core microbiomes. To ensure consistent sponge-microbe associations and accurate identification of planktonic bacteria transmitted from seawater, we were very restrictive with the definition of the sponge core microbiomes (present in all the replicates), and with the identification of valid biological 16S rRNA gene sequences (100% sequence identity) that belonged to potentially different bacterial taxa. We found a high overlap (>50% relative abundance) between the sponge species core microbiome and the seawater bacterial core in ca. a half of the studied species, including representatives of both, HMA and LMA sponges. From our restrictive analysis, we point to horizontal transmission as a relevant way of symbiont acquisition in sponges. Some species-specific recognition mechanisms may act in sponges to enrich specific seawater bacteria in their tissues. These mechanisms would allow the maintenance of bacterial communities in a species across geographical ranges. Moreover, besides contrasting preferences in bacteria selection from seawater, divergent physiological traits may also account for the different microbiomes in species of HMA and LMA sponges.