I think it is likely (20% or greater) we will compete for resources against non-terrestrial lifeforms before humans leave the solar system, assuming we leave the solar system.
Earth doesn't contain the majority of all water in the solar system. Earth might not even contain all of the liquid water in the solar system. What are the chances that liquid water exists in Ceres' core, or under the icey surface of Europa or Ganymede or another moon? What are the chances that Martian ice, or Europa ice, or Saturn's ice have microbes frozen in them, possibly able to thaw given better environmental conditions? We might even find life in places without water, such as Titan's methane lakes. Titan has a methane cycle very similar to Earth's water cycle. Methane makes a great rocket fuel. Water makes great rocket fuel and is necessary to life support systems.
We have a history of taking what we want without regards to the consequences or whom it hurts. If we don't compete with other life when we leave Earth it's because other life isn't out there, not because of our strong morale core.