I can't recall ever seeing an organ in a Reformed Baptist church. It seems that most use a piano or sing a cappella. But I haven't seen organs in most Presbyterian churches either. Most of the ones in this part of the country are relatively small. So some of that may simply have to do with the size of the congregation. Nice organs aren't cheap, and accomplished organists usually aren't either. Likewise, it may be that some smaller congregations (Presbyterian, Baptist or whatever) don't have a choir simply because they don't have enough people to form one and not because they oppose choirs out of conviction.
In the 19th Century, at least in the USA, pianos were often associated with saloons. There are tales of members of Baptist churches taking the piano out of the church and throwing it into a lake or somewhere similar when attempts were made to introduce them into the churches. But organs apparently were OK in many of those churches, if not all of them.
I'm surprised that no one has mentioned the hymn singing controvrersy among early Baptists. The Particular Baptist leader Benjamin Keach was instrumental in gaining widespread acceptance for hymn singing in Baptist churches. I don't know much about it, but apparently the idea that some had was that congregational singing was no more appropriate than using a prayer book. But in that case, it seems that Keach's main opponent(s) opposed congregational singing entirely.
Here are a few resources quickly turned up in a search:
Samuel Renihan message on the controversy
Passage from James Leo Garrett's Baptist theology
https://feileadhmor.wordpress.com/2011/04/06/baptists-initiate-congregational-hymn-singing/
Passage from
Pure Worship: The Early English Baptist Distinctive, a book with an interesting title with which I'm not familiar.
But seriously I remain unconvinced because the work of the Spirit in the context of the passage and throughout Ephesians clearly refers to New Testament revelation. 
