Does "a matrix of $L$ with respect to $\color{red}{\text{S and T}} \,$" signify $[L]_{T \leftarrow S}$ or $[L]_{S \leftarrow T}$? Call a linear transformation $L.$ Because conjunctions commute, $\color{red}{\text{S and T}}$ is ambiguous. The two examples beneath both answer with $[L]_{T \leftarrow S}$ , but why can't $\color{red}{\text{S and T}} \implies [L]_{S \leftarrow T}$? 
Source: Linear Algebra by David Lay (4 edn 2011). p. 294. Section 5.4. Question 28.

Let $V$ be a vector space with a basis $B=\{b_{1},\ \ldots,\ b_{n}\}$, let $W = V$ with a basis $C=\{c_{1},\ \ldots,\ c_{n}\}$, and let $I$ be the identity transformation $I$ : $V\rightarrow W$. Find the matrix for $I$ relative to $B$ and $C$. What was this matrix called in Section 4.7 ?
Answer: We want $[I]_{C \leftarrow B} =$ changes of coordinates matrix from B to C. [...]

Source: Elementary Linear Algebra with Applications (9 edn 2007). p. 398. Section 6.3. Q10.

Let $L: P_1 \to P_2$ defined by $L(p(t)) = tp(t) + p(0).$
  Consider the ordered bases:
  for $P_1$, $S =$ [irrelevant], $S' =$ [irrelevant];
  for $P_2$, $T =$ [irrelevant], $T' =$ [irrelevant].
  Find the representation of $L$ wrt (a) S & T (b) S' and T'.
Answer: (a) Answer wants $ [L]_{T \leftarrow S}$. (b) $[L]_{T' \leftarrow S'}$

 A: Let $V$ and $W$ be vector spaces with ordered bases $\mathcal{B}$ and $\mathcal{B}'$, respectively. Let $T \colon V \to W$ be a linear transformation. We can talk about
$$
\text{the matrix of $T$ with respect to $\mathcal{B}$ and $\mathcal{B}'$}
$$
without ambiguity because of the prior set up of the notation. We mean the matrix associated to $T$ when we choose the ordered basis $\mathcal{B}$ for $V$ and the ordered basis $\mathcal{B}'$ for $W$, and not the other way around. If you only focus on the words "$\mathcal{B}$ and $\mathcal{B}'$" without taking into account the fact that they have been defined as bases of $V$ and $W$, respectively, then there it appears ambiguous.

Having said all this, in my opinion it would definitely be better to say something like
$$
\text{the matrix of $T$ with respect to the pair of ordered bases $(\mathcal{B},\mathcal{B}')$}
$$
instead of "$\mathcal{B}$ and $\mathcal{B}'$". One reason is, take the case when $V = W$, as in the question details. Then, one needs to be extra careful to keep in mind which basis is attached to the domain and which one to the codomain, especially when we are loosely asked for the matrix of $T$ with respect to "$\mathcal{B}$ and $\mathcal{B}'$". In any case, it can't hurt to be precise in one's definitions.

However, it is also worth noting that even though "conjunctions commute", as noted by the OP, this is not always the case outside mathematical logic. Consider the sentence
$$
\text{I brushed my teeth and had breakfast.}
$$
This has a different meaning compared to
$$
\text{I had breakfast and brushed my teeth.}
$$
Similarly, the sentence
$$
\text{the matrix of $T$ with respect to $\mathcal{B}$ and $\mathcal{B}'$}
$$
can be thought of as being written in a slightly colloquial/non-technical/non-rigorous manner, with a different rule of grammar being applied than "conjunctions commute".

Lastly, while it is not ideal, it is still good practice to be aware of such abuses of notation, since they are common. Another abuse of notation is when the term "ordered basis" is shortened to "basis". The ordering is important when talking about the associated matrix, but authors often use the term "basis" to implicitly mean "ordered basis" whenever required.
TL;DR. Yes, this is ambiguous but only slightly. Such ambiguities are common, so it is good to be aware of them. If possible, try to avoid them in your own writing for greater clarity.
