Rail-to-rail oscillations in subtractor op amp circuit
This is a pretty fast op-amp.  It's almost certainly due to layout or decoupling.  

Do you have ceramic decoupling caps right at the supply inputs to a ground plane?  Is this on a PCB with short traces and a tight layout or is it on a breadboard?  

If it's the latter you might want to try a lower bandwidth op-amp.  Since your differential gain is 1 but your noise gain is 2, you need an amplifer with a gain bandwidth of say 10MHz or so.  (Assuming the 1MHz signal is the highest frequency you need to work with.) 

This is a 300MHz amplifier, which is probably making your life more difficult than it needs to be.