Unexpected results when using @extend for themes

Extends, as you’ve already discovered, can get rather messy. I would go about solving your problem by using an @content aware mixin in combination with global variables (this uses mappings, which are part of 3.3… you can do it with lists of lists, but it’s a little less elegant):

$base-color: null; // don't touch
$accent-color: null; // don't touch

$sections:
    ( household:
        ( base-color: #ffc933
        , accent-color: white
        )
    , sports:
        ( base-color: #f7633e
        , accent-color: white
        )
    );


// the mixin to output all sector specific css
@mixin sector-css() {
    @each $sector, $colors in $sections {
        $base-color: map-get($colors, base-color) !global;
        $accent-color: map-get($colors, accent-color) !global;
        &.sector-#{$sector} {
            @content;
        }
    }
}

.product-paging {
    @include sector-css() {
        h2 {
            background-color: $base-color;
        }
    }
}

Output:

.product-paging.sector-household h2 {
  background-color: #ffc933;
}

.product-paging.sector-sports h2 {
  background-color: #f7633e;
}

Update: Since you want to guarantee that the sector class is always at the top, you just need to switch around a little.

@mixin sector-css() {
    @each $sector, $colors in $sections {
        $base-color: map-get($colors, base-color) !global;
        $accent-color: map-get($colors, accent-color) !global;
        .sector-#{$sector} {
            @content;
        }
    }
}

@include sector-css() {
    &.product-paging {
        h2 {
            background-color: $base-color;
        }

        h3 {
            background-color: #CCC;
        }

        h2, h3 {
            color: $accent-color;
        }
    }
}