Why do single, double and triple bonds repel each other equal amounts?
The way you have learnt to predict molecular geometries is called the VSEPR theory. As all theories, it makes assumptions and has a certain number of limitations. The issue you are asking about is one such limitation.
When predicting the geometry of molecules with VSEPR, one should treat multiple bonds as a single entity. However, the geometry obtained is just a first approximation, or “idealized” geometry. In fact, multiple bonds induce distortions from this ideal geometry, pretty much like lone pairs do (I assume you know that already. If not, well, check the above-linked Wikipedia page for “lone pair”.) Citing from this online course:

Multiple bonds contain a higher electronic-charge density than do single bonds, so multiple bonds also represent larger electron domains (&quot;fatter balloons&quot;). Consider the structure of phosgene, Cl2CO, which is shown below.

From the Lewis structure of phosgene, we might expect a trigonal planar geometry with 120°-bond angles. However, the double bond seems to act much like a nonbonding pair of electrons, reducing the ClCCl bond angle from 120° to 111°. In general, electron domains for multiple bonds exert a greater repulsive force on adjacent electron domains than do single bonds.

So: yes, lone pairs and multiple bonds give rise to deviations from the ideal VSEPR geometries. It's nice that you figured it out on your own!