The vast majority of large social movements have their origins in the left. Climate change, most social justice movements, the push for higher minimum wage, immigration reform, etc.
In general, people leaning 'right' are less interested in social initiatives on the whole. In the US, one of the most common talking points from the right is the desire to be 'left alone' by the government or social movements.
The only issue the right seems to really be organized about (in the US) is guns, and that's because a huge percentage of military folk lean that direction.
Large grass roots social movements are not the only way to be organized though. I agree that the left seems to better be able to capitalize on that type of movement in recent history, but i dont think it follows that the right is disorganized, just organized differently. (Then again this is the trump ers and he is not really the establishment right wing im thinking of-To me at least he seems to be riding a wave of fairly disorganized [but powerful] right wing populism, so maybe you are right in regards to him)
In general, people leaning 'right' are less interested in social initiatives on the whole. In the US, one of the most common talking points from the right is the desire to be 'left alone' by the government or social movements.
The only issue the right seems to really be organized about (in the US) is guns, and that's because a huge percentage of military folk lean that direction.