Here is an example of someone misreading Poincare to argue that he believed in the aether. A 2006 paper, Can science advance effectively through philosophical criticism and reflection?, by Roberto Torretti, says:
In the highly acclaimed electrodynamic theory — or ought we to say theories? — of Lorentz, the ether is completely motionless and its mechanical structure and behavior — if it has any — is of no concern at all. As Whittaker lucidly wrote: “Such an aether is simply space endowed with certain dynamical properties” (1951/53, 1:393).That's right. Today people try to put down Lorentz's relativity by calling it Lorentz aether theory, instead of electron theory, as it used to be called. It did not depend on the aether, as noted here and here.
It is therefore no wonder that, despite Lorentz explicit warning to the contrary,50 the general public, including most philosophers and even some physicists, identified his ether with Newton’s absolute space, or at any rate assumed that it was at rest in it.51 Still, the idea that this elusive form of matter was part of the furniture of the universe had become deeply entrenched during the 19th century, and nobody seemed willing to dismiss it. Surely it is not easy for a highly respected profession to admit that one of its time-honored terms of art is a noun without a referent.52 Even Poincaré, who in 1889 had predicted that “the day will doubtless come when the ether will be rejected as useless”,53 at the Paris Congress of Physics of 1901 argued thus for believing in it:Poincare did not argue for believing in the aether. He argued that it was a mathematical convenience. His philosophy is often called conventionalism because of opinions such as this.We know where our belief in ether comes from. If we receive light from a distant star, for several years that light is no longer at the star and is not yet on the Earth. It must therefore be somewhere, sustained, so to speak, by some material support. The same idea can be expressed in a more mathematical and more abstract way. What we record are the changes suffered by material molecules; we see, for example, that our photographic film displays the consequences of phenomena staged many years earlier in the incandescent mass of the star. Now, in ordinary mechanics, the state of the system under study depends only on its state in an immediately preceding state; the system therefore satisfies differential equations. But if we did not believe in the ether, the state of the material universe would depend not only on the immediately preceding state (l’état immédiatement antérieur), but on much older states; the system would satisfy finite difference equations. To avoid this derogation of the general laws of mechanics we have invented the ether.54[Footnote 54] Poincaré (1901b); translated by me from Poincaré (1968), pp. 180-181. I cannot repress the feeling that Poincaré the mathematician must have known (i) that if a given physical state depends on another in accordance with a system of differential equations, none of the two states can immediatelyprecede (or follow) the other one, and (ii) that time dependent vector fields can be defined on space without assuming a material support for them to sit on. I suppose (ii) is the reason why he talks of inventing the ether at the end of this tirade about believing in it.
This is a point that mathematicians grasp immediately, but physicists and philosophers have a lot of difficulty with. Poincare was a mathemetician. Mathematicians frequently define concepts for mathematical convenience, regardless of whether they are physically observable.
Anyone who says that Poincare believed in the aether fails to grasp that simple point.