Modular Addition in RC5 is linear or not?
Consider $f: x\mapsto f(x)=\underbrace{x+x\ldots x}_{a\text{ times}}+b\bmod 2^{32}$ in the the ring $(\mathbb Z_{2^{32}},+,\times)$, where $a$ and $b$ are constants.
Per one meaning, $f$ is linear, that is of the form $x\mapsto a\times x+b$, for constants $a$ and $b$. Per another meaning, $f$ is not (in general) a linear boolean function. $f$ is also not linear in the field $(\mathbb F_{2^{32}},\oplus,\otimes)$, where $\otimes$ is polynomial multiplication modulo an irreducible polynomial of degree $32$.
To make «the rotations are the only non-linear operator in RC5» true, we can craft a meaning of «linear» that allows any of the above definitions.
Without rotations, RC5 would be trivially breakable no matter the number of rounds, for lack of propagation from high-order to low-order bits of the four 32-bit sub-blocks.
It's harder to prove the (true) assertion that with only fixed rotations, and baring much more rounds, RC5 would be breakable. That's because it would be too linear, in some sense that I fail to exactly define.