Should we consider $\mathsf{P} \neq \mathsf{NP}$ a law of nature?
Strassen's statement needs to be put into context. This was an address to an audience of mathematicians in 1986, a time when many mathematicians did not have a high opinion of theoretical computer science. The complete statement is


  For some of you it may seem that the theories discussed here rest on weak foundations. They do not. The evidence in favor of Cook's and Valiant's hypotheses is so overwhelming, and the consequences of their failure is so grotesque, that their status may perhaps be compared to that of physical laws rather than that of ordinary mathematical conjectures.


I am sure that Strassen had had conversations with pure mathematicians who said something along the lines of 


  "You're basing the whole of complexity theory on a house of cards. What if P=NP? Then all your theorems will be meaningless. Why don't you just put forth a little effort and prove that P$\neq$NP, rather than keep building a theory on such weak foundations."


In 2013, when P$\neq$NP has been a Clay prize problem for a dozen years, it may seem difficult to believe that any mathematicians actually had such attitudes; however, I can personally vouch that some did. 

Strassen continues by saying that we should not give up looking for a proof of P$\neq$NP (thus indirectly implying that it is indeed a mathematical conjecture): 


  Nevertheless, a traditional proof would be of great interest, and it seems to me that Valiant's hypothesis may be easier to confirm than Cook's... 


so maybe I would label it as a "working hypothesis" rather than a "physical law". 

Let me finally note that mathematicians also use such working hypotheses. There are a large number of mathematics papers proving theorems whose statements run "Assuming the Riemann hypothesis is true, then ...".