Simply by appearing to be attacked by the left, Musk gets interest/support from the right (or, at least, the not-left). The old right is dying, literally, from a demographic perspective. With the gradual removal of the current dead-weight (heh) of conservative boomers, the right is necessarily going to shift from reactionary paleo-conservatism to something else.

The right's skepticism of science is substantially (but not entirely) directed towards science institutions not the scientific method per se, i.e., conspiracies are hiding the real science. Although Musk is not to the right, he comes across as turning over entrenched institutions (the good old boy clubs of the space and transportation industries). As long as Musk doesn't overtly attack the right, they may be broadly supportive.