Showing that someone sympathizes with white supremacists is not "to make someone look bad."
Context matters and you're ignoring it.
I feel like that's the fallacy of association. Just because they give a platform for everyone to speak, including white supremacists, does not mean that they agree with them or their values. It's just a byproduct of the actual values that they do have, in this place giving everyone the right to speak. As such, by giving everyone the right to speak, that just naturally means you'll get a lot of good but subsequently a lot of bad. I would argue that's just natural, and isn't particularly something to avoid. Once they start banning such people then they start going against the values they agree with.
When it comes to the concept of hate speech, while I disagree with the general term and the semantics of it, free speech does have its legal limits. In terms of offensive speech, free speech is unprotected, according to the Supreme Court, when it "tend to incite an immediate breach of the peace" which is usually done by provoking a physical altercation. However, the word needs to be a "personally abusive [word] which, when addressed to the ordinary citizen, is, as a matter of common knowledge, inherently likely to provoke a violent reaction." However, the most important part is that such speech must be "directed to the person of the hearer" and because of that is "thus likely to be seen as a 'direct personal insult.'"
Not to mention that of course, true threats of violence that are directed toward an individual or group of people with the intent to place the person or persons involved at risk of immediate bodily harm or death are normally not protected under the first amendment (you can't yell bomb in a plane, fire in a theater, or say anything that might cause someone to believe you're about to either physically hurt or kill them).
Reddit bans any speech that "glorifies, incites, or calls for violence or physical harm against an individual or group of people." This complies with the true threat of violence exception to the first amendment.
As such, if we were to go to the extreme and talk about a reddit page which encourages white supremacy and discusses steoreotypical stuff like how great they are and how awful other people are, such a page would technically not be against either Reddit's rules or against the free speech exceptions to the first amendment. As long as such a thread does not directly glorify (which I will admit is probably the one that flies under the radar most I would say, an example would be something like a photo of people burning and romanticizing it, but I'm pretty sure reddit in general has NSFW rules, I don't know if there's any white supremacy threads so I don't know how often such things happen there), incite (usually seen as starting or stirring up violence, which probably doesn't happen if everyone in that thread agrees with themselves), or call for violence (such as planning an attack or basically saying that they need to hurt people soon/in general), then it is safe under free speech. Also, in such a scenario you can't use the first example I gave either because people saying racist remarks among themselves that are not directed at you or are addressed to anyone in particular do not meet the criteria necessary to disqualify it as free speech (in this case the criteria would be the remarks being "addressed/directed to the ordinary citizen/person of the hearer"). So, even if you consider it personally abusive and a direct personal insult, it does not matter because it needs to be addressed or directed at you, and unless it is, it is still protected by the first amendment. Interestingly, in both cases (both the reddit rules and the criteria needed for the speech in question to be an exception to free speech), there did not appear to be anything wrong with the advocation and/or agreement with violence and as such the advocation/agreement of violence appears to be protected by both reddit and the first amendment. However, I will admit I need to do some more research there.
I did a quick search to see if I can even find any white supremacy reddit page (stuff like r/whitesupremacy which apparently used to be a thing but isn't there anymore). So I took a look at all the headlines on the first page of The_Donald and I couldn't find anything that meets any of the aforementioned criteria needed to be not protected by the first amendment. Granted I will be fair and say I didn't look too far into the comments, but even then I doubt such criteria would be met. Even if there are people who make mean or even racist remarks, the reality is that it is still protected by the first amendment and Reddit's rules. The racist remark would have to clearly and explicitly meet the aforementioned criteria and/or break one of the aspects of Reddit's rules for it to be an issue, which even then can be even more difficult to do once you consider that agreeing with violence/advocating violence could possibly be protected under both.
Note:
Let me be clear, I stated all of this not because I agree with, condone, support, or think anything positive about white supremacy or racism, but rather I make this argument for two reasons. The first, is because I genuinely find it fun to play the devil's advocate and argue an unpopular opinion, I do not like it when everyone just kind of has the same reaction or thoughts on something, if everyone is agreeing then nobody is thinking (as the famous quote says). I think it is interesting to have a genuine discussion and talk with other people and see as well as share a plethora of perspectives (and I would hope my history would generally show that as well as my willingness to admit when I am ignorant on an issue or at least feel like I am, wrong when it comes to my facts/argument, can't find any holes in an argument, and actually agree on points I agree with in order to find common ground, among other things). Lastly, I would say I somewhat agree with the values of Reddit (granted I don't know their history or if they've been hypocritical when it comes to maintaining said values so I plead some ignorance there and I apologize), I feel like everyone should be allowed to speak under any circumstance no matter what even if I completely disagree with or hate what they're saying and/or their ideologies. Of course that will lead to both great and awful people having voices, but I truly feel that is what's best and I have faith in people to truly make the right decisions (or at the very least make the decisions they think are right to them and pursue their happiness regardless of what I feel about them, as long as they don't infringe upon my rights such as physically hurting me or meeting the criteria for their speech to be unprotected, among other things). I apologize, normally I don't really get this defensive but given that I know the general demographic of Resetera, the topic of this thread, and I suppose just a vibe that I'm getting, I just want to make sure I lay myself and my intentions all out there because I frankly just want to have a reasonable discussion with differing opinions where we can discuss our ideas and focus on the merits of the aforementioned ideas and the arguments presented. Also, I apologize if I've made any grammatical errors, given the length of what I wrote and the fact it's 4:37 AM for me I might not reread this immediately. Thank you for reading all of this and for your time.
Edit: I don't know how I made all these lines through everything, can someone help? I'll try to fix this immediately.
Edit 2: Right now I'm just deleting and rewriting everything. I'm on mobile so it'll take some time.
Edit 3: I did it! Ended up figuring out, I'm glad I was able to fix it since that really made me start to panic since I didn't want to make things potentially even worse for myself. Apologies, everyone.