Being RR is helpful, because you can eliminate almost all other plants going into the mix. Almost no other grasses or other broadleaves pass through the herbicide. This will reduce the number of noxious or toxic weeds in the hay or haylage.
Also important to dairy farmers is the control of many undesirable broadleaves, which can change the lignin content of the ration. Lignin is indigestible and limits other useful-cell digestibility. Lignin is a component in plant stem production, and can be very high in plants like giant ragweed and woody-like weeds. If these enter the ration, they can nullify some of the usefulness of the rest of the meal.
Conventional alfalfa (meaning non-RR) is more likely to have volunteer weeds, as most broadleaf herbicides are non-selective, meaning if they will kill black nightshade (very toxic to horses) it will also kill some of your alfalfa, which then opens the crop canopy for new weeds to grow.
Most RR Alfalfa is only sprayed with glyphosate (aka RoundUp) one time - and that is when the alfalfa and the initial weeds are 3-4 inches tall. After that, the alfalfa has usually taken over, and provided enough cover, that other weeds don’t germinate. If there are weeds that germinate, a good alfalfa stand will out perform (since they are more established), and choke them out. However, it can be used in “rescue” situations, such as excess rainfall preventing timely hay cuttings, and new germination flushes.
Also, in some RR Alfalfa planting situations, the use of glyphosate means that direct no-till seeding (not disturbing the soil) can be used, because any existing weeds can be exterminated in one spray pass. This means a healthier, more productive soil, with less erosion. It also means that an oat or rye cover crop may not have to be used. On occasion, these small grains can bring in undesirable weed seeds.
Hope that helps! Let me know if you have more questions!