Are all isotropic bandpass filter kernels, wavelets?
Certainly not. ,,Isotropic'' means that the impulse response is independent of direction, that is, that the filter is rotationally symmetric. Wavelets are orthogonal basis functions (filters, maybe) with certain properties. Not every orthogonal basis function will be isotropic, and not every isotropic filter is orthogonal. It is even hard to see how a isotropic filter may be a wavelet.

Look up ,,wavelet conditions'' to learn more about how this orthogonality has to be understood to build an invertible transform. Banded Matrices with Banded Inverses might help the algebraically inclined.