The RIP routing protocol was published in 1988 and uses Bellman-Ford algorithm to calculate shortest path. Also more recent version of RIP (RIPv2 and RIPng) use the same algorithm. The Djikstra algorithm was published in 1959. Why RIP use Bellman-Ford instead of Djikstra? More generally, why routing protocols prescribe specific shortest path algorithm, could they be parametrics how the short path is calculated?
Bellmon Ford is used by distance vector routing protocol (DVR). In DVR technique router keep knowledge of only next router which is adjacent that's why exchange of routing database only with neighbors. So in DVR no need of shortest path. But in DVR every router implicitly will able to find shortest path very slowly after stabilize. The main drawback of DVR technique is slow convergence and count-to-infinity problem.
But to keep the knowledge of entire topology router needs every other router's (neighbors as well as non-neighbors) routing database, because of first convergence and remove the count-to-infinity problem. So from one router to reach another we need shortest path algorithm. In this scenario link state (OSPF) routing protocol is example which does multicasting as well unicasting.