The last time I tried searching for podcasts in Malay, I also only found religious ones. So, I went searching again and found some things.
Bernama Radio 24 Some news podcasts from bernama.com
ERA PodcastSelamat Malam Singapura Live Sadly there seems to be only two episodes.
MHTV This has only one episode and most of it is music but there's some talking in between too. I might be useful.
Ok, so this one is in Indonesian but I'm sharing it anyway for those focusing more on Indonesian.
BBC IndonesianI think your best bet might be to try to find a talk radio show. I don't know if this will work but you can also try finding a talk show or celebrity interview on youtube or somewhere, rip the audio, and listen to that.