Yes, but that's the broader understanding, not related to religion. You can even find somewhat bizarre (to my ear at least) examples like "ecumenical meal of German, Italian, and Chinese dishes", but it's a turn of phrase, and not necessarily applicable in the religious context.
In the religious context the very same Merriam-Webster you just quoted defines ecumenism as:
"a : of, relating to, or representing the whole of a body of churches
b : promoting or tending toward worldwide Christian unity or cooperation"
It's kind of like you can have a coding or eating marathon... because in broad sense it's defined as any "long-lasting or difficult task or activity"... but then you still shouldn't call a 10-mile run "marathon".
https://www.oxfordlearnersdictionaries.com/definition/englis...
"involving or joining together members of different branches of the Christian Church"
https://dictionary.cambridge.org/dictionary/english/ecumenic...
"encouraging the different Christian Churches to unite"
The same in encyclopedias:
https://www.britannica.com/topic/ecumenism
"ecumenism, movement or tendency toward worldwide Christian unity or cooperation. The term, of recent origin, emphasizes what is viewed as the universality of the Christian faith and unity among churches."
https://en.wikipedia.org/wiki/Ecumenism
"Ecumenism (/ɪˈkjuːmənɪzəm/), also spelled oecumenism, is the concept and principle in which Christians who belong to different Christian denominations work together to develop closer relationships among their churches and promote Christian unity."
("Not to be confused with Interfaith dialogue", correctly points out the article).
But maybe I'm just a purist. (Not a native English speaker either, if that matters, although the term is rather universal and not really exclusive to English).