  We prove a well-posedness result for stochastic Allen-Cahn type equations in
a bounded domain coupled with generic boundary conditions. The (nonlinear) flux
at the boundary aims at describing the interactions with the hard walls and is
motivated by some recent literature in physics. The singular character of the
drift part allows for a large class of maximal monotone operators, generalizing
the usual double-well potentials. One of the main novelties of the paper is the
absence of any growth condition on the drift term of the evolution, neither on
the domain nor on the boundary. A well-posedness result for variational
solutions of the system is presented using a priori estimates as well as
monotonicity and compactness techniques. A vanishing viscosity argument for the
dynamic on the boundary is also presented.
