The question requires indeed a very serious scrutiny. This is because, the goal expressed by the OP has already been put into practice in 2019. In that year, a private organisation sent a payload of tardigrades to the Moon, the Beresheet mission.
The OP explains that the motivation, similar to that of the experiment embarked on the Israeli’s mission, is (apparently) to study Life. Quote from the question: “it would be a great experiment that would also tell us which mutations will occur over time in that environment[Mars]”. So, they (the OP, the Arch Foundation, ...) wanted to do it in the name of Science. It would be indeed “great” (in the sense that we may be able to learn new things), PROVIDED it is conducted scientifically. And this is exactly where the OP of this question didn’t show due considerations.
First, “in that environment” assumes the prerequisite that we have scientifically characterized the environment, and further we have, and can maintain strict control over it (nothing else get in after the start of the experiment).
Second, to study the mutations triggered by a certain environment condition requires that we have a pretty good knowledge of the various mechanisms of mutations under various conditions (that we can or cannot parametrize). I doubt scientists can claim that we have reached that level of knowledge.
Third, “will occur over time” means that we have that time to observe these phenomena, or at least we know the time frame. This can be problematic when it can take thousands years, as the case for some undersea microbes to replicate.
In short, this type of ideas/proposals should be pushed back categorically: people can do terrible things in the name of Science.
To the author of this question, to be clear, I am not insinuating dark motives from you. I am making a plea that you reconsider your position.
I would like to address the recent clarifying Edit
Why this is considered anathema?
Submitting life forms from Earth to conditions found on other celestial bodies has inherent scientific values (nothing anathema about it).
What is very disputable is the approach you suggest: instead of taking precautions to not spreading Earth’s life by cleaning the landers, do the opposite. What you suggest is akin to using an entire celestial body (or an unbounded area of it) as a laboratory for some random experiments, open-ended in their expected outcomes, and decided by some individuals. This is unscientific at best, and dangerous for sure, since I bet people would use this as a pretext to justify their sloppiness (and/or to save money).
As to the second part of your question, where you ask whether we should put on equal footing, on one hand, the preservation of some “native” forms of life, on the other hand, the spreading of Earth life, it can be viewed from different angles. From the point of view of "ethic", I personally find it anathema (same debate as destroying jungles to grow industrial crops, same debate as destroying archeological sites to build modern housings). In general, I don’t find it so urgent to spend billions in colonizing other planets. I prefer that we spend the same on preserving ours, such as cleaning the oceans of the plastic wastes.
But to avoid the “opinion-based” criticism so favored on SE, we can look at it from the scientific perspective. Perhaps you are thinking that, if there is a native form of life, we can let Earth’s forms of life compete with it. We take the winner, what do we lose? I think, in case the Earth life out-competes a native form, we lose forever the knowledge of how much alien forms of life can teach us, about our origins, about our destiny, about the definition of “life” itself. It is a big lost to Science. In the case the native form is the winner, we can cross-fingers it doesn’t evolve into a super Earth-killing pathogen.