Not sure about your first criterion, but about the second one, I think interloper would be a good fit, even though it is not necessarily an idiom.
One who intrudes in a place, situation, or activity
By the way, to lope is to run or ride with a steady, easy gait. The word interloper is therefore kind of idiomatic. An interloper in the discussion that does not concern him or her is just loping along as if there's nothing wrong, pretending they belong in the discussion, despite their presence being neither needed nor appreciated.
Word History: The word interloper has its origin in the time when England was embarking on the course that would lead to the British Empire. Interloper is first recorded in the late 1500s in connection with the Muscovy Company, the earliest major English trading company (chartered in 1555). The word was soon being used in connection with independent traders competing with the East India Company (chartered in 1600). The East India Company was established as a monopoly, and independent traders, called interlopers, were not welcome. The term is probably partly derived from Dutch, the language of one of the great trade rivals of the English at that time. The inter- is simply the prefix inter-, which English has borrowed from Latin, meaning "between, among." The element -loper is probably related to the same element in the word landloper, "vagabond," a word adopted from Dutch landloper: land, plus -loper, from lopen, "to run, leap." The word interloper came to be used by the 1630s in the extended sense of a "meddler, a person who intrudes in others' affairs."(Minor modifications in this entry are mine.)