I was trying to change the translation from "Mien Piej" to "Start" but the software pointed out that it would break long established wikis. Is this true? Can it be changed without creating problems? Thanks!

No it can't. Not unless every wiki that it is using this as their main page currently adds an override to set that message back to the original value

Are there many wikis using this content language?

In T266743#6588170, @Reedy wrote:

Can it be changed without creating problems?

No it can't.

Does that mean this task should be declined? (What kind of software change is being asked for in this task?)

Does querying wikiapiary help?

If this query is correct Has language::jam, there's no public wiki with language "jam" registered with wikiapiary

I'd be willing to change the text and put a RELEASE NOTES entry for the breaking change. As a bonus it would be nice to have a support from other translator(s) in this language but looking at https://translatewiki.net/wiki/Special:SupportedLanguages/jam I don't see other active ones.