I don't know that Heinlein qualifies for being not woke. I Will Fear No Evil is a tranny fantasy, Friday is pure Girl-Power, the same again for Glory Road. All of his books containing Lazarus Long have enough incest to satisfy G. R. R. M. (Long marries his mother in To Sail Beyond the Sunset.) Beyond This Horizon is a satire of the second amendment and capitalism. Job: A Comedy of Justice is just Atheism+. Heinlein himself toured the USSR during the 60's, and Asimov remarked that Heinlein was a "flaming Liberal" during the 1930's, all of which puts his works in question. That being said, "Inside Intourist", and "Pravda Means "Truth"" are still worth a read, if only to see what is coming for the US. None of this is to say that Heinlein is not one of the Great Science fiction authors, merely that he is not even close to being conservative.

As for the Hugos, don't bother, they have always been woke and they were really bad even before 2013 (John Scalzi was nominated in 2009). I spot checked a few of their earlier years. For example, Ursla K. Le Guin won in 1970 (beating out Larry Nivien), and she is every bit as bad as some of TheImpossible1's "favorite" authors. G. R. R. M. was also getting nominations if not Awards as far back as at least 1975.

If you want fiction that isn't woke, you are gonna have to read stuff that is pre-1960's. Pre-WWII is even better. Some specific examples are Robert E. Howard (Do read his Solomon Kane stories, not just Conan. Don't bother with Conan from other authors.), H. P. Lovecraft, and the greatest science fiction writer: E. E. "Doc." Smith. Read the Lensman series, and the Skylark series for sure.