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A I Don’t Want It T Shirt – though somewhat indirect and subtle – method used for stars that do not fit into these categories (which is the majority of them, at least in our own galaxy) is as follows: First deduce the likely temperature and size of the star from its dominant colour and the atomic spectra present in its light (temperature is related to colour, and different chemical elements are produced under different conditions of temperature and pressure, which in turn depend on the mass and age of a star). From these we can work out the likely luminosity. From the luminosity we can deduce the stars absolute magnitude [1] (i.e. how bright it would appear at a standard, fixed distance of 10 parsecs from us). Comparing this with the star’s apparent (i.e observed) magnitude, we can then calculate it’s actual distance from us. To me, this method of deducing a star’s distance from us merely by studying its light, and then doing a few calculations based on thermodynamics, nuclear physics, atomic physics and stellar dynamics, represents one of the most beautiful examples of the power of human ingenuity and careful, deductive reasoning in the history of science.

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The description from Richard Muller quoted in the question is a simplification of reality meant to help people better visualize how the I Don’t Want It T Shirt of spacetime works. In reality the galaxies are moving through spacetime in a complex fashion, based on the combination of all the forces acting on them, primarily the gravity of nearby galaxies and galaxy clusters. In the case of the Milky Way and Andromeda, these two galaxies are part of a gravitationally bound cluster of galaxies, called the Local Group. The dominant force that determines the movements of objects within the cluster is the combined gravitation of all the mass in the cluster, and not the expansion of spacetime. In other words, the gravitational attraction that the Milky Way and Andromeda have for one another that is drawing them together is stronger than the expansion of spacetime between them that would otherwise push them apart, and thus attraction wins and the two galaxies are on a collision course. In the same vein, the gravitational force that holds the earth in orbit around the sun is stronger than the expansion of spacetime between the earth and the sun (the expansion of spacetime at that distance being very small), and so the earth’s distance from the sun is not increasing for that reason. Likewise you are not flying apart because the molecular bonds holding the atoms in your body together are stronger than the minuscule expansion of spacetime between them in your body. The Local Group as a whole, however, is moving away from other galaxies and galaxy clusters to which it is not gravitationally bound, due to the expansion of spacetime.

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