Your primary responsibility in a software project is to make this particular software project stellar.
Your backyard, your problem. If the problem lives in someone else's backyard, the problem is primarily theirs. If everyone lives by this, and truly cleans up their own backyards to make them clean and spotless, things will be great.
Of course, sometimes you need to cooperate with your neighbor to figure out exactly whose responsibility it is to fix that fence between your backyards, as it might not be totally obvious who owns the problem, and maybe you even disagree or in some cases both blame the other party.
To get that backyard in such a great shape that you want to show it off when you have friends over, you cannot accept having a broken or dirty fence just because you cannot agree with your neighbor. You roll up your sleeves and you fix it. No matter whose fault it is.
Sometimes, the best way to make your project excel is for you to join in and help out in related projects. If your project depends on or uses another project, it might be wise and clever to join that project to at least monitor what is going on there and see what you can do to help it steer in the right direction.