There is a bit of a conundrum regarding this since some consider redbud roots as non-invasive while others consider them as potentially invasive. But to settle the clout, redbud roots are considered as non-invasive because the tree produces a shallow root system in general.
The taproot of redbud trees spreads at the same length as their canopy spread, however. This is the reason why it is recommended that redbud trees be planted at least 25feet away from the home’s foundation because some redbud types have longer spread. And although the roots are not as thick as other deciduous trees, it could still pose potential damages to the home’s foundation, if ever.