The properties of electrons in the heliospheric plasma are modulated by various factors, starting with the expansion and bimodal nature of the slow or fast solar wind, and continuing with the kinetic mechanisms of acceleration and energy exchange with small-scale plasma waves. The role of wave-particle interactions can be understood through rigorous kinetic modeling based on observational data. This paper presents a refined evaluation of the instabilities triggered by temperature anisotropy, that is, whistler and firehose instabilities, taking into account for the first time the correlations between the electron core and halo populations revealed by in situ observations. In establishing core-halo correlations, temperature anisotropies \$(A)\$ and plasma beta parameters \$\left({\beta }\_{\Vert }\right)\$ are of interest, as quantifiers of free (kinetic) energy at the origin of instabilities. These correlations incorporate the mutual effects of the electron populations and enable a realistic characterization of instabilities, in terms of either the core or the halo parameters. The instability thresholds can be significantly reduced under the mutual core-halo effects, and comparisons with observations prove the constraining role of self-generated instabilities, not only for the core but also for the halo electrons. The most relevant are the results for the slow solar wind, for which both the parameters and the core-halo correlations are less affected by the strahl component, which is otherwise more prominent in the fast wind. In high-speed winds, temperature anisotropies are more confined, most likely under a stronger effect of fluctuations generated by the electron strahl whose properties are not yet quantified to allow a similar analysis.