I think as general principle, one Bible believing church should respect the discipline of another.
As Presbyterians, we have very specific process in regards to this, but am not sure how it might be worked out in other communions.
The types of discipline ordinarily are:
1) informal admonishment
2) formal admonishment
3) suspension from Lord's Supper
4) deposition (from office)
In practice, I wouldn't see #1,2 or 3 ever unilaterally communicated by the home church to another church outside the denomination. Normally, these are all done privately and confidentially within the church, not announced to the church as a whole, not even the home church. Steps #4 would likely be communicated within the denomination and step#5 might be more publically communicated.
However, #3, #4, #5 might be communicated if another church inquired or sought to receive that person for membership, though. These might be akin to a Christian "living a disorderly life" or not being a member in good standing. Someone in that category ought not take the Lord's Supper anywhere unless and until they repent.
Post Tenebras Lux; "And the seventh angel sounded; and there were great voices in heaven, saying, The kingdoms of this world are become the kingdoms of our Lord, and of his Christ; and he shall reign for ever and ever." - Revelation 11:15