The question "is Algebra really needed if my child is not interested in math/science?" comes up now and then among homeschoolers. Here's what I think:
Algebra is essential. Not everyone will solve equations for a living. But you need to be able to think in terms of "functions" - meaning how one thing varies as a result of a change to another thing on which the first thing is dependent. To have an intuitive sense of this is priceless. Algebra trains this type of thinking. "Functional" thinking works in politics, relationships, science, finances, etc - really in all of life.
Algebra is just learning to convert various functions into different forms so they can be understood and manipulated more easily. This idea of "transforming" one problem into another type is also essential. Some problems are truly unsolveable as presented, but clever rethinking may show how it can be solved from another perspective - another essential life skill!
Algebra is wonderful to train proper thinking, as there is always an "objectively" correct answer - not a subjective "I think/you think" impasse common to so many of the "soft" sciences.