Both ElasticSearch and Redis, overkill usecase?
You should consider using RediSearch. Using RediSearch can provide you a solution for your needs, getting both Redis performance and a full-text support.
Elasticsearch and redis are basically meant to solve two different problems, As one does indexing while other does caching.Redis is meant to return already requested data as fast as possible whereas as Elasticsearch is a search and analytics engine, it would perfectly fit a use-case where you have to implement a fast search engine and it will be more performant than any in-memory data structure store or cache such as redis(Assuming your searches will be complex, will involve some aggregation/filters).
The problem comes profile updates Since your profile updates are not that frequent you could actually do partial updates to the ES index rather doing reindex.So whenever a person updates its profile get the changeling set(changed data) and do a partial update to the particular document in ES Index. You can see how its done here partial update.
This one particular stackoverflow answer will help you cache vs indexing