I am not an astrophysicist, but my understanding is that due to the expansion of the universe and the speed of light, the volume of space we will ever be able to access is finite, roughly that of the galactic supercluster we're in.
For all practical matters, I think it can be considered infinite. (And the theoretical limits might not be fixed either)
But the question is always, how much of that is within our reach.
Currently nothing out of earth on an economical base. So I also see the point we have to set priorities.
But currently there is a big focus on war, rather than climate change etc. and with more crisis, people tend to think even more short term. Space on the other hand can give that long term thinking effect, that can people make consider whether fighting for the limited ressources on earth is the only way. And maybe instead unite forces for benefit of all of mankind (and possibly life itself).
This isn't even close to true. In addition to what the other comment points out about eventually losing causal contact with all parts of the observable universe that aren't already gravitionally bound to the same supercluster as the Milky Way, even something like breadth-first search of the entire local supercluster at near the speed of light would take more time than the local supercluster will still exist. The universe will run out of hydrogen and stars won't exist any more long before you can cover all of even the tiniest portions of infinite space.
No. For all practical matters, accessible space is FINITE, and actually gets smaller all the time due to accelerating expansion of the universe. In about 150 billion years all galaxies outside the Local Supercluster will pass behind the cosmological horizon.
"For all practical matters, accessible space is FINITE"
I think, this is what I said:
"But the question is always, how much of that is within our reach."
Currently that is only earth. With some steps up, you can have all the other planets in this system plus the asteroid belt. Step further up and you have lots and lots of other star systems, the cosmological theoretical limits you are citing are not really an issue on the timeframe that matters to us - space tech is and the limits how fast we can make rockets, or find other ways to take a short path.
