However, more often than not now, due to a rapidly changing climate, that is not what happens.
This means that, for the majority, we humans have shelter from the elements, we subject our food-bearing plants to the rigours of the great outdoors and can do no more than hope for a good weather year.
However, more often than not now, due to a rapidly changing climate, that is not what happens .
Massive floods, long droughts, hurricanes and severe monsoons take their toll each year, destroying millions of tons of valuable crops.

more often than not and more often than not now? what are they difference?

does 'that is not what happens' means Nothing happens except Massive floods, severe monsoons...?

Question

However, more often than not now, due to a rapidly changing climate, that is not what happens.
This means that, for the majority, we humans have shelter from the elements, we subject our food-bearing plants to the rigours of the great outdoors and can do no more than hope for a good weather year.
However, more often than not now, due to a rapidly changing climate, that is not what happens .
Massive floods, long droughts, hurricanes and severe monsoons take their toll each year, destroying millions of tons of valuable crops.

more often than not and more often than not now? what are they difference?

does 'that is not what happens' means Nothing happens except Massive floods, severe monsoons...?

Answer

"More often than not" vs "More often than not now:

Using now implies that it's something that happens now, but was different before. 
• eg I used to go the the gym a lot, but more often than not now I stay at home.
Without using 'now', it sounds like it is something which has been true for a long time. With 'now', you are emphasising a change.

"That is not what happens":

It is related to what came before, in this case 'a good weather year'. Humans hope for a good weather year, but now this is not what happens; good weather years have gone (or a less frequent) because of climate change (and you see monsoons, floods, droughts, etc.).

Hope that helps!

Answer

It's not very well written. I had to read it a couple of times to work out what it means. 
It would be clearer with another comma - 'more often that not, now, there...' The 'now' is just emphasising that they are talking about the current situation.
I think that 'that is not what happens' is directly referring to 'good weather years'. They then refine that to mention the extremes of floods and storms etc.