Monopole flux is the key property of flux tubes proposed to be behind various astrophysical structures. Is there any direct evidence for this? Evidence has emerged for the existence of giant clouds with size about 100 AU in the vicinity of the supermassive GBHE of Milky Way (see this and this). These objects - called G objects - look like gas clouds but behave like stars. G objects stretch longer when nearer to GBHE but get their original shape when farther away. One would expect that they are torn apart by the enormous tidal forces created by GBHE.
The identification could be as visible matter assignable to a spaghetti like structure formed by monopole like flux tube, which could have also produced the visible matter in the thickening of the flux tube. By flux conservation the monopole flux prevents the flux tubes from splitting even in the huge gravitational field of supermassive GBHE. Without monopole flux tubes to which visible matter is gravitationally bound the structure would be torn to pieces. In Maxwellian world monopole flux tubes are not possible. In biology the behavior of gels (the contents of an egg is the basic example) could be based on monopole flux tubes connecting the cells together.
See the chapter Cosmic string model for the formation of galaxies and stars or the article A model for galaxy formation.