I don't think it's being used here as a generic term for an "open" church, to which all are welcome, or as an "open-minded" or non-dogmatic kind of church, though the name clearly suggests both these ideas. The speaker doesn't say "asistía a una iglesia abierta"; he/she says "a iglesia abierta". I think very probably refers to a specific church: the Ministerio la Iglesia Abierta Inc., based in Barceloneta, PR, one of the enormous number of Christian churches in Puerto Rico. Here it is on pp. 19-22 of this list of Iglesias Cristianas en Puerto Rico:
https://data.pr.gov/api/views/vi6y-e3sa/rows.pdf?app_token=U...

Here's its website:
http://ministeriolaiglesiaabierta.es.tl/Home.htm

It's also got a Facebook page.

As a proper name it won't be translated, though you could put a literal translation ("Open Church") in parentheses afterwards if you think it would be helpful.