Type Ia supernovae are not standard candles in the sense that all such supernovae have the same luminosity. This is also the case for other standard candles such as Cepheids.
What we can say, is that type Ia supernovae appear to have a peak luminosity that can be calibrated using other, distance-independent, observable properties.
Indeed, the intrinsic luminosity of type Ia supernovae probably varies by as much as a factor of four. The underlying physical reasons for this are not yet fully understood but almost certainly include the type of progenitor (e.g. whether it was a double white dwarf), the detailed composition of the exploding white dwarf, and in particular, how much $^{56}$Ni is synthesised in the explosion and ultimately powers the light curve.
The standard procedure at the moment is to apply empirical corrections to the "raw" absolute magnitude that depend on the width/shape of the light curve (the so-called "stretch correction"), the colour of the light curve and the stellar mass of the host galaxy - all of which have been found to correlate with the peak luminosity of the explosion. There are many papers discussing these corrections, but a good starting point is Hauret et al. (2018).
After applying these corrections, the dispersion of the corrected peak luminosity is about 0.1 magnitudes - turning these objects into "standard candles".
It may be that a significant fraction of the type Ia supernovae are caused by merging white dwarfs. However, some theoretical studies (e.g., Pakmor et al. 2024) suggest that the explosion of the more massive white dwarf dominates the light curve shape and evolution and the smaller white dwarf may not explode at all. These then might fit neatly into the calibration scheme described above. Nevertheless, there are certain subclasses of type Ia supernovae, that exhibit peculiarities in their spectra or light curves, that are usually excluded from standard candle analyses. Whether these peculiarities stem from the nature of the binary companion or the spin and magnetic field of the exploding white dwarf is still debated (e.g. Axen & Nugent 2023).