In two Higgs doublets models (2HDM) we revise the conditions that Yukawa matrices must obey to guaranty the absence of flavour changing Yukawa couplings. The study of the evolution of these conditions under the one-loop renormalization group reveals that such general flavour conserving (gFC) structures, in the leptonic sector, are fully stable. This suggest to analyse two different types of 2HDM: those that are gFC in the leptonic sector and type I or type II in the quark sector. These models introduce in a minimal way lepton flavour universality (LFU) violation at the same time that decouple, for example, the muon and electron sectors. We apply those models to understand simultaneously the electron and muon (g-2) anomalies. We find two types of solutions compatible with all experimental constraints from LEP and LHC, from LFU, from flavour and electroweak physics and compatible with the theoretical constraints in the scalar sector. The solutions need the Z2 symmetry of the Higgs potential to be softly broken. There is a solution where both (g-2) anomalies are understood by two loop graphs with tan𝛽~1, and all the scalars in the 1−2 𝑇eV range. This solution appears in both models. There is another solution, with relevant one and two loop contributions, with scalars bellow 1 𝑇eV, and large tan𝛽, the second scalar Higgs has a mass in the range 0.2−0.4 𝑇eV and the charged and pseudoscalar bosons are degenerate and heavier than the new scalar. This solution just appears in the model that in the quark sector is type I.