Handling features with multiple values for clustering
You can easily use get_dummy function in Pandas to convert them to numerical vectors. 

The idea is that categorical variables do not have a numerical intuition e.g. when it comes to the definition of Distance. But just imagine you have one feature Genre with 3 values Comedy, Romance and Crime. Then you can model them in a 3-dimensional space by saying Comedy = (1,0,0), Crime = (0,1,0) and Romance = (0,0,1). It replaces 1 feature with three but intuitively works well.

Update

I just understood your question after editing it! It was a bit fuzzy previously. But I keep my initial answer and add an update.

In this case use the values of the feature Genre (unique values of union of all genre sets in that column) as new features and determine their presence with 1 and 0 otherwise. Should work.

Movie_ID    Action  Thriller  Drama  Romance  Comedy

1             1       1         1       0       0
2             0       0         0       1       1
3             1       0         0       1       0