fibre is important but it's present naturally in meat and milk. not present in eggs btw. lactose acts as fibre when its not digested, and goat and sheep milk have a lot of both soluble and insoluble fibre in them, neatly suspended.
processed meat has less fibrous material in it, especially if it's been treated with nitrates and nitrites, these damage the structure of the sinew and such that functions as fibre in meat digestion.
it's a myth that sausages cause constipation, ffs the intestines they are (or used to be, mostly) wrapped in are fibrous and help encapsulate things. they put a lot of raw potato starch in most sausages so that's a problem there. again, chemical additives and processing techniques affect this.