With a few PiecewiseExpand
it gives a solution:
Pf[r_, \[Rho]_] :=
Piecewise[{{K*(\[Rho][r])^(
5/3), \[Rho][
r] < \[Rho]low}, {(\[Rho]high*c^2 -
K*\[Rho]low^(5/3))/(\[Rho]high - \[Rho]low)*\[Rho][
r], \[Rho]low <= \[Rho][r] <= \[Rho]high}, {\[Rho][r]*
c^2, \[Rho][r] > \[Rho]high}}];
MassEqf = (M'[r] == 4 \[Pi] *\[Rho][r]* r^2);
PressureEqf = (\[Rho]'[r] PiecewiseExpand[
D[Pf[r, \[Rho]], r]/\[Rho]'[r]] ==
PiecewiseExpand[-((
G*(M[r] + 4 \[Pi]*r^3*Pf[r, \[Rho]]/c^2)*(\[Rho][r] +
Pf[r, \[Rho]]/c^2))/(r^2*(1 - 2*G*M[r]/(r*c^2))))]);