First off, my response is assuming that you are using either the sandbox or paid version of the premium Search APIs.
The query that you presented will read as such:
climate AND change OR red OR blue AND from:user1 OR from:user2
Based on your explanation of what you are looking to do, I suggest that you use the following query instead:
“query”: ""climate change" OR red OR blue (from:user1 OR from:user2)"
If you used the example that you included, it would look for Tweets that had ‘climate’ and ‘change’, but not specifically right next to each other. This could be…
The change in the climate.
By wrapping the two keywords with phrase quotes, it would just match Tweets that had ‘climate change’ next to each other in that exact order.