Autism

I'm just trying to communicate in a way that works for me

Maybe try communicating in a way that works for them? This isn't autism, it's narcissism.

When I was younger, I used to fall into this pit-trap myself. The big problem is language and communication just don't work like you'd want it to.

What you intended don't really matter, it's all about other people's interpretations of your intentions. So when you say:

"can you not let the dogs tangle?"

Your bluntness leaves an uncertainty in their interpretation of your intentions, which they will fill in with your serious tone as being minorly aggressive and accusatory. Naturally they will take offense at that.

Those platitudes exist to eliminate that uncertainty, to make sure that their interpretation of your intentions matches more closely to what they actually are. It works great for neurotypical folks as most of them have a natural intuition using these platitudes (or not using them to cause offence.).

We have to do much more to learn what those folks grasp naturally, and it can be a source of stress. It's part of what causes my social anxiety, as even now I'm not particularly great at reading the cues neurotypical folks give off, so I struggle to come up with a timely response.

I just try to remember to preceded or follow anything I say with please.

"Please don't let the dogs tangle."

I felt so extremely frustrated when a friend made a huge deal of how "I thought I was always right and nobody else counted". Okay, fair enough, but explain further since that doesn't sound nothing like me. I had taken his opinion into consideration and changed my mind tons of times.

Turns out I had to precceed any statement about politics with wich he didn't agree with "in my opinion" or something like that. Every. Single. Time.

It's especially frustrating as it's completely meaningless. Of course it's my opinion and not someone else's. Of course I believe it's probably right, otherwise it wouldn't be my current view on the topic.

"Can you not let the dogs tangle?" sounds like you're telling people what to do. Normies typically get offended by that because they wanna feel like it's for them. If you rephrase it to sound like they're doing it for you they may be more receptive. "I'm worried the dogs might get hurt, would you stop them from tangling?"

I just don’t understand why I have to say “hey, would you mind not letting the dogs tangle? thank you:)” in some high pitched voice when I could just say, “can you not let the dogs tangle?” in a tone that conveys I’m serious. it’s so much easier when intentions are simply stated.

I think part of your problem actually starts even earlier, because it exists in both examples. You use you-statements. Neurotypicals hate these and feel directly accused of something. So softening the you-statement helps.

If it makes sense to you and comes more easy you can try something that is also taught to neurotypicals who look into learning about communication: Avoid you-statements and instead use I-statements that are about you and the situation, not them and the situation.
There are a lot of resources about that on the internet (because as said, even the Neurotypicals need to learn about that) but here's one example where they explain the difference and how it's perceived

But here you'd instead say "I don't like when the dogs tangle". Neurotypicals will see a problem that needs to be solved and go like "hey, I can help" instead of becoming defensive about the perceived accusation that they did something wrong. It's not a guarantee that it works but studies show a lot higher acceptance for I-statements.