I encountered this issue on a production environment of one of my clients.
Several List View web parts were shown on a page.
If I entered a search term in either one of them, the last web part would filter the results.
I tried readding them, moving them, copying them to another page, nothing worked.
I noticed I didn’t have this problem on the test environment.
While investigating the difference between, I came across following post which explained my situation.
The versions on the different environments were:
Production version: 15.0.4569.1000 (2013 SP1)
Test version: 15.0.4693.1000 (February 2015 CU)
Eventually, by updating the production environment to the latest CU, the problem was solved!