How can I transform a collection into a Guava Multimap grouped by the elements of a nested collection property?

You can use custom collector for this:

Multimap<String, Foo> map = list.stream().collect(
    ImmutableMultimap::builder,
    (builder, value) -> value.getTags().forEach(tag -> builder.put(tag, value)),
    (builder1, builder2) -> builder1.putAll(builder2.build())
).build();

This does not cause extra side effects (see here on this), is concurrent and more idiomatic.

You can also extract these ad-hoc lambdas into a full-fledged collector, something like this:

public static <T, K> Collector<T, ?, Multimap<K, T>> toMultimapByKey(Function<? super T, ? extends Iterable<? extends K>> keysMapper) {
    return new MultimapCollector<>(keysMapper);
}

private static class MultimapCollector<T, K> implements Collector<T, ImmutableMultimap.Builder<K, T>, Multimap<K, T>> {
    private final Function<? super T, ? extends Iterable<? extends K>> keysMapper;

    private MultimapCollector(Function<? super T, ? extends Iterable<? extends K>> keysMapper) {
        this.keysMapper = keysMapper;
    }

    @Override
    public Supplier<ImmutableMultimap.Builder<K, T>> supplier() {
        return ImmutableMultimap::builder;
    }

    @Override
    public BiConsumer<ImmutableMultimap.Builder<K, T>, T> accumulator() {
        return (builder, value) -> keysMapper.apply(value).forEach(k -> builder.put(k, value));
    }

    @Override
    public BinaryOperator<ImmutableMultimap.Builder<K, T>> combiner() {
        return (b1, b2) -> b1.putAll(b2.build());
    }

    @Override
    public Function<ImmutableMultimap.Builder<K, T>, Multimap<K, T>> finisher() {
        return ImmutableMultimap.Builder<K, T>::build;
    }

    @Override
    public Set<Characteristics> characteristics() {
        return Collections.emptySet();
    }
}

Then the collection would look like this:

Multimap<String, Foo> map = list.stream().collect(toMultimapByKey(Foo::getTags));

You can also return EnumSet.of(Characteristics.UNORDERED) from characteristics() method if the order is not important for you. This can make internal collection machinery act more efficiently, especially in case of parallel reduction.

ImmutableMultimap.Builder<String, Foo> builder = ImmutableMultimap.builder();
list.forEach(foo -> foo.getTags().forEach(tag -> builder.put(tag, foo));
return builder.build();