There are two claims here: microbeads are environmentally harmful, and microbeads are not necessary.
First claim: environmental harm:
This is a summary of the environmental science from the Canadian government. TL;DR: yes they are harmful, but probably not very harmful. Fish ingest them and then excrete them. However inverterbrates seem to suffer more harm, and its quite possible that if you eat shellfish then you will wind up eating microbeads. Toxicity is due to ingredients in the plastic leaching out, and here it gets complicated. Read the report for all the details.
Second claim: they are not necessary. This is probably true, but I can't find any specific evidence. It would seem reasonable, though, that you could get the same effect by just using a slightly rougher face cloth.