Does the existence of two independent stocks $$ dX_1=r_1X_1 dt+ \sigma dW_1 $$
$$ dX_2=r_2X_2 dt+\sigma dW_2 $$ with $r_1\gg r_2$, $\sigma>0$ and independent Brownian motions $W_1,W_2$ contradict any common market axiom? In particular, in the case $r_1>r_2+\mu$ where $\mu$ is the interest rate of a bond, I would expect that such a market cannot exist in reality, since I cannot imagine anyone being interested in selling $X_1$ to buy $X_2$ in such a market.
If we had $W_1=W_2$ then an arbitrage opportunity existed, so the two stocks could indeed not coexist in realistic markets. However, I don't know if the same intuition transfers to the case of independent Brownian motions.
"In reality" there is no Wiener processes, nor geometric Brownian motions, neither independence.
I suspect that by "realistic" market you mean arbitrage-free. Then yes, this model is realistic as it is arbitrage-free in the usual sense. Denoting $r$ the risk-free interest rate, the martingale measure on $[0,T]$ is given by $$ \frac{d\mathrm{P}^*}{d\mathrm{P}} = \exp\left\{ \frac{(r-r_1)W_1(T)+(r-r_2)W_2(T)}{\sigma} -\frac{(r-r_1)^2 + (r-r_2)^2}{2\sigma^2}T \right\}. $$