I'll challenge the phrase "semantic noise" a little bit. It makes me think of fluffy language, extra words thrown in that add little (if any) additional information (somewhat related note: grandiloquent was my favorite English word for a long time). That doesn't sound like your problem here. What you are describing is specific terms not being understood by the people you're speaking to, causing them to be unable to understand what you're saying. It's not a question of cutting out distracting, useless words, nor of making your point more quickly or explicitly. Instead it seems to be a matter of correctly assessing your audience and being prepared to make mistakes in those assessments.
1. Assess your audience
Different people have different functional vocabularies, and it is very difficult to determine whether or not a certain person will know a certain word without presenting it to them. It is also hard to get a sense of your own functional vocabulary, so "matching" someone else can be hard. That said, with people that you have known for an extended period of time it is possible to get a sense of how they talk, which I have found to be an excellent model for how to talk to them effectively. If my cousin always describes something oily as "oily" and never as "oleaginous", I'll try to only use the former. (I avoid "oleaginous" anyways, but that's a whole different topic).
2. Pick the right level of abstraction
Most jargon comes into play when summarizing a broad swath of information so as to allow fluid discussion. Outside of a more formal discussion you may be able to use less precise language. For example, when speaking with people outside of my department at work I almost always say "average" or "simple average" instead of "mean", even though a lot of people would understand "mean" in that context. I almost never say "arithmetic mean" because, while it's a very precise description it's also one that most people are not familiar with, and it makes a distinction (as from "geometric mean", etc.) which most people don't need to worry about most of the time.
3. Try to balance complicated ideas with complicated descriptions
Some ideas are very complex, and are casually referred to in more short-hand, vague ways. To say "immune system" is easy, and many people will have a good idea of what you mean when you say it, allowing you move on and discuss something more specific like infections, or autoimmune disorders, or a cytokine-storm immune response. They've already learned the one phrase, and so are ready to handle additional information. But there is a limit to how much information a person can absorb all at once, and so if you find yourself having to describe what an immune system is, then there might be a ceiling on much detail it's going to be possible to convey. You can fill in some of the gaps with analogy and iterative explanations, but there are limits. More complex, new information tends to mean less detail and a shallower discussion.
I feel stupid when I try to present the "puppet show" version of an idea, but if I don't feel there is an alternative that's what I'm left with. I used to have to explain health insurance policies to people a lot for work, and so my clients heard a lot about an analogy involving a bath tub, bucket, and faucet. I'd generally preface it with something like
I know this example might seem a bit silly, but people have found it clearer than the policy contracts in the past.
That helps get around the "why are you talking to me like you think I'm an idiot" response, and reiterates that I'm going for maximum understanding, not trying to comment on the person with whom I'm speaking.
4. Check in often
It's very difficult to assess what words another person will know without having witnessed it directly, as in (1). Using more succinct language assumes that the listener already has a certain degree of working knowledge, and being confronted with an expectation that you know something you do not can be jarring, especially if it happens over and over again over the course of a single conversation. So when I'm trying to describe something and think that my audience might get lost I try to check in at each conceptual "step":
OK, so imagine a bath tub, and inside that tub is an empty bucket sitting right below the faucet. Now, if we turn on the faucet, water will start flowing into the bucket, but none into the tub, right? In this example, the water represents your medical bills. The bucket represents your deductible, which you will have to pay yourself, and the tub outside of the bucket represents bills that your insurer will help you pay. So as water comes out of the faucet, it's going to fill up the bucket first, right? Keeping that image in mind, we can see that your bills will end up in different categories based on how much you've been billed so far... [and it goes on like that for a bit]
It's not a great example, but the bolded words are pauses where you can ensure that your listener is following you so far and offer more explanation if not. I've had good results with that sort of sequence, because it emphasizes that I want to make sure the listener understands each piece so that we can move on to the next piece. Regularly checking to make sure that you've sufficiently explained each piece makes it clear that you want the other person to understand what you're saying and are not assuming any particular knowledge on their part, lessening the impression that you want to demonstrate how much you happen to know that they do not.
As a bonus, this has also helped me fine-tune my assessments from (1). The real-time feedback on how my descriptions and explanations are working with various people has really helped me to examine assumptions that I've made and evaluate changes that I try out.
5. Assume that miscommunications are always your fault
I went back and forth on including this one, but it's a standard I hold myself to and I feel it provides the right mindset for addressing this type of issue. If I have subject knowledge that another person may not, then it's up to me to find a way to express it. It's never that your audience is too ignorant (or anything else, even if I may privately feel that that is the case), it's that I have failed to find a way to explain things clearly, and it's my job to find a better approach when one is failing. If, after a couple of tries, I'm just not conveying the message, I typically apologize for having explained things poorly. It can be humbling and frustrating both, but I think that it's done a lot to keep other people from feeling that I'm showing off.