I agree that the designation of “hate group” and even the concept of hate speech is potentially fraught. The SPLC has to take their responsibility very seriously when they make these designations. I haven’t seen compelling arguments that they don’t, but the bar should be very high.
Re Probe Ministries, I visited their site and read just one of the posts by Sue Bohlin. It was vile religious crap, exactly the kind of stuff that got me started on my journey to freedom from Christian faith. (Phrases like “gay agenda” and “political correctness” are, for me, giant red flags.) I would never go anywhere near an organization that teaches such things, and we donate to organizations that attempt to undo the damage that this stuff does.
BUT. SPLC is reasonably clear (IMO) about criteria that distinguish obnoxious opinions or odious beliefs from what they would call hate. You can read about the criteria on their site (thanks @Chris_Falter). The article that I read at Probe crossed the line, clearly in my view. It has the usual blather about marriage and sin and “idolatry” and drips with judgmental cheap shots. Disgusting, yes, but that’s not why I think it earns the label of “hate” in the political context that (I think) SPLC emphasizes. It crosses a line (for me at least) by claiming that same-sex marriages endanger kids, and by embracing and endorsing gay conversion “therapy.” Either of these things disqualifies the organization as credible, and justifies, to me, labeling it as something more dangerous than just “some confused religious people reading old sacred books selectively.”