- I'm not a graphic designer
- I don't like stars
- I think green on red is a stupid choice
This whole thing is giving me trouble and I'm out of ideas at what to come up with.
Of course! What did you expect? Started with such a negative predisposition of course you have neither arrived nor come to anything with this logo.
Let's try to reverse the problem, if it exists.
I'm not a graphic designer
That's the biggest problem, but not yours. The problem is for the people who are asking you for your services as a designer knowing that you are not. You have not any tool to deal with, and the biggest problem will come after, a simple logo is just a starting point. But if they insist it's something you must deal with.
I don't like stars
I wonder what kind of stars you don't like: four points stars, five points stars, six points stars, seven points stars, fifteen points stars, angled stars, rounded stars, long ray stars...? Big stars or small stars? Don't you think it's to extreme to say "I don't like stars"?
Anyway, if a client says my logo must have a star, there are many graphic ways to make this star, has not to be a star shape over a typography.
We return to the previous point, you are not graphic designer, reason why you don't have the sufficient tools as to dominate the subject of a star added to a logo.
I think green on red is a stupid choice
We, the graphic designers, tend to have a lot of respect for our work tools and the terminology we use. A color combination is never stupid, on the contrary, there are elements that we usually use as contrast and harmony, or adjacency and complementarity, or cold and warm combination, or saturation, tint and brightness. Well, data that a designer knows because work with them assiduously. I don't think in my case I am capable of saying that using a certain language to code is a stupid choice, since I am not a programmer.
Absolutely all colors are part of our day to day, and there's no stupidity in them. Who claims that a combination of colors is stupid, obviously is not a designer, and could never work with any color since he/she does not know them.
But, answering your question, there are many possibilities of using red and green in a medical image. In fact it is the basic combination in what refers to medical health: the fluid that gives us life and its complementary, normally used in medical uniforms for that reason. Maybe you are just imagining the color at its highest saturation, but both red and green have many variables in tone, saturation and brightness. Did you ask why they want red and green?
Hospital logo example from pngimage.net
RED, BLUE AND A STAR. This is the Madrid Health's logo base system: blue for sanity and red for the community flag, the star is a part of this flag:
Finally, the designers usually like when the client give us the elements to use, as many of us, as part of our profession, we usually start from very structured bases to challenge and break them. But it's something that only a professional knows how to do.