Hmm, fair question.
I wouldn't describe it as anti-woke, I mean I listened to it for a good few months without realising that Chris mainly got famous as an anti-SJW and I was pretty surprised when I found out.
You'll hear Colin go after the media occasionally, calling them a hive mind and saying that they couldn't wait to kick him out as the only conservative but it's usually just in passing and when it's relevant. He doesn't sit there and go on 20 minute rants about the problem with games media for no reason.
With actual games, I can't remember them ever critiquing a game for being too woke. Actually the opposite, I recall someone writing in and asking if Naughty Dog had an SJW agenda and both Colin and Chris dismissed it saying that just because a character is a lesbian, it doesn't automaticlaly make it an SJW storyline. Colin also once said as well that you shouldn't criticise a developer for including progressive themes or else you're no better than those who hate on games for what they don't include - e.g minority characters etc.
As for your politics / world view point, Sacred Symbols definitely isn't an apolitical podcast. Recently they were discussing the sexual harrassment allegations and said most people are probably telling the truth, hear them out but don't go attacking anyone. With the BLM protests they supported the message but condemned the rioting / looting. Usually they take a pretty balanced view, at least in my opinion. Despite what you'll hear, Chris is pretty left leaning and while Colin is economically conservative, he's at least in the middle when it comes to social issues.
As someone who's pretty conservative, I don't always agree with what they say but it doesn't bother me because they're not preachy and don't deal in absolutes. I mean, I can't imagine them calling me a piece of shit just because I don't agree with them which isn't something I'd say about most people in the industry. Colin's also at least open to hearing other perspective - he had a black YouTuber called Mama Micah on recently because she took issue with his criticism of BLM and he wanted to discuss it. Can't imagine any of these woke outlets doing the same.
Also, the political / current events discussions are usually at the beginning of the podcast, it's not dragged into the video game discussion. What really pissed me off with my Giant Bomb and Unlocked examples is that they're letting their politics affect their viewpoint on the actual game. Acting as if a Harry Potter game, of all things, is going to struggle because of some comments that literally nobody outside of their social bubble takes any issue with.
I remember Colin was talking about being pro-abortion once and ackowledging that a good chunk of his audience disagree whereas I genuinely get the sense that these journalists are deluded enough to think that they speak for their entire audience.