Are these products substitutes or independent?
The goods are perfect substitutes because the marginal rate of substition between them is constant for all values of $x$, $y$ and $m$, i.e. there is $c \in \mathbb{R}$ such that
$$
\forall (x,y,m) \in \mathbb{R}_+^3: \ MRS_{x,y}(x,y,m) = - \frac{MU_x(x,y,m)}{MU_y(x,y,m)} = c.
$$
This essentially means that the goods $x$ and $y$ are so much alike that the rate of substitution does not diminish.

The total quantities may be limited, but (I think) perfect substitution has nothing to do with set of feasible allocations or the budget set, only with the preference ordering.

Varian defines perfect substitutes in subchapters 3.4 and 4.3. Neither subchapter considers feasibility.