I don't like being harmed. I don't like harming other people. Do you like being harmed or harming other people? I presume not.
So let's call harming people "immoral", let's try to avoid doing it, and let's make laws to prevent people from doing so.
There you go, that's pretty much the gist of it.
If there is someone who wants to harm others, other people can agree on laws or other things to impede their ability to do that. One could potentially also discuss this with them, try to break down the reasons why they might want to harm others, appeal to their empathy or make the case that if they harm others (except out of self defence), then others are more likely to want to harm them, or at least be less concerned about harming them (which they probably wouldn't want).
* That's a very rough summary of the basis of morality under moral subjectivism.
To put it more formally: moral subjectivism is the view that there is no objective morality. We subjectively determine our moral values. These values can vary from one person to the next (as indeed they seem to). This doesn't entail basing one's morality on harm reduction, but I can decide on this moral value given our my empathy and the desire for self-preservation and peaceful coexistence, and I can try to convince others of the same moral value by appealing to similar emotions and desires that they may have.
There are also other secular moral frameworks.
What's the basis for morality under theism?
I'm fine with agreeing there's no objective morality under atheism, but I'm not convinced that can exist under theism either. "Objective morality" sounds like a contradiction in terms to me - it seems incoherent to me to say you "should" do something without following that up with a "because" to explain why you "should" do it. And that "because" can vary from one person to the next, and potentially from one situation to the next. So I don't even know how objective morality is something that could exist.
Theism may have externally-imposed morality via a deity, but all theists can really do is to slap the "objective" label on said morality, whereas it doesn't seem to make much sense to me to do so.
Theism has the "biggest stick" argument, i.e. what God says is moral because they have a really big stick that they'll hit you with if you don't do that. I'll agree that there's a sense of what you "should" do there (if you want to avoid that punishment), but I don't know that I'll call that "morality", as much as I'll just call that "law". A government might throw you in prison if you break laws, but that doesn't mean all laws are moral.
If you want to call that in itself morality, then what God commands could be entirely arbitrary. He could drown a whole lot of men, women, and children, or he could tell you to go out and slaughter a bunch of people, and that would be moral merely because he says or does it (and I didn't just make up those examples, although one might say someone did).
Theist say morality might be "written on your heart", or that you might be made with a specific sense of morality. But one could say our genes and upbringing do the same. Why should we do the thing that's been "written on our hearts"?
Atheists can say: well, we shouldn't always do that. Some people have a sense of morality where it's okay to go around murdering people. We decide what we should and shouldn't do through reasoning, not by just doing whatever we want to do. Theists who make this argument have more of an issue saying that.
And this is not even going into all the reasons why I think theist claims are unjustified. Without those claims being true, all of this falls apart even further. Whereas if we follow secular ideals, we can still make the most of this life even if a god exists (but of course if that god wants to torture us for all eternity if we wear mixed fabrics or whatever, it would be important to try to figure out whether that's true).
People are going to disagree and do bad stuff either way
Theists like to act like theism solves the problem of moral subjectivism, but it simply factually and demonstrably doesn't.
Theists (even from just one religion) vehemently disagree about the morality of a whole lot of things. Views on morality within any given religion has changed significantly over time.
You could say a god has an unchanging morality, but if there is such a god who's tried to tell us what is and isn't moral, they've clearly done such a poor job, that we pretty much need to figure it out by ourselves in any case.
Also (much like I told you in the past), Nazis aren't a great example for a theist (especially a Christian) to use in this argument, because Nazis were overwhelmingly Christian (only 1.5% atheist). Soldiers had "God with us" as a slogan on their belt. Atheist left-wing organisations were banned. Hitler said "Secular schools can never be tolerated because such schools have no religious instruction". Himmler didn't allow atheists into the SS. I wouldn't say Nazism is inherent to Christianity, or anything close to that, but it very directly challenges the idea that Christianity can prevent this from happening ... because they were Christian and promoted Christianity. Maybe you'd say they weren't "true" Christians, but then you have to argue theology, and it all gets very messy (and very much not objective).
Fighting for a better world is a long and constant struggle. There will always be bad people, and there's always a risk that you yourself may be blinded by one's harmful desires. We need to always be vigilant, stand up for what's right and fight against those who wish to harm others. This isn't something we can just easily fix by using the correct worldview. It is hard work no matter what, but we have made a lot of progress through discussion and protests and promoting empathy and critical thinking and challenging bad ideas. Saying "my religion is the only thing that can fix it" seems demonstrably false, doesn't really help get us to a better world, and achieves little more than making yourself come across as thinking you're better than everyone else.