How can "threshold questions" such as standing be crucial to the outcome of a constitutional case?
While I agree with the previous responder that courts sometimes use standing to avoid deciding cases, standing has been an important part of American jurisprudence for many years.
Part of the basis for standing is Constitutional. Court may only adjudicate "cases or controversies," meaning they cannot make a decision without a legitimate grievance and cannot make a decision on a hypothetical situation. That means that the party who comes to the court seeking a solution must be the party who was harmed. Otherwise, there is no case or controversy. Another aspect of the doctrine of standing is more practical. Courts could not function efficiently if anyone could go before the court to assert a general claim on behalf of other people. Finally, the doctrine of standing has a common sense basis because when the court presents a solution for others who are not before the court, the outcome affects people who have not asked for an adjudication. I cannot go to court and ask the court to make a decision that would affect the life of another person or entity because only that person or entity should be able to do so.
So, while standing can give a court some wiggle room, it is based upon sound Constitutional principles and inherently practical, sensible ideas. Parties who do not have a case or controversy and who have no harm or right to assert before the court simply should not be in court.
These can be crucial to the outcome of a constitutional case because they give courts a way out of having to decide on the actual constitutional question itself.
The Supreme Court, in particular, doesn't always want to have to rule on the actual constitutional questions, so they sometimes "punt" and rule on threshold questions instead.
The best recent example is the Pledge of Allegiance case Elk Grove Unified School District v. Newdow. In that case, Newdow wanted the Court to rule on whether the phrase "Under God" should be in the Pledge.
Instead of ruling on that (which would be hugely controversial) the Court ruled that Newdow lacked standing because he was in a custody battle over his daughter and so couldn't really represent her interests.