I am an undergraduate who is determined to attend grad-school, and as such, I am hungry for opportunities to demonstrate my academic worth. In a recent course, my dialogue with the instructor naturally extended, and soon he gave me materials and open problems on which I made progress/results that impressed him. After some more work, he offered to co-write and publish a paper with me on the topic.
Now, this particular instructor holds a very unpopular opinion (not ethically) that is his own novel work, which of course he is proud of, because if were to be true, it would have grand implications. Personally, while recognizing that I am not nearly as knowledgeable as he is, I strictly disagree with his opinion. Most second opinions I read online disagreed on similar grounds to mine.
Unfortunately, he will almost certainly mention it in our paper, likely quite a few times. I have tried to *very lightly* bring up my disagreement as a matter of "please teach me why I am wrong about this", and he did not seem to take to it well. Additionally, sometimes in his papers, he uses language I think is too grand flowery while making claims I think are too broad and slightly unestablished.
On the other hand, he has been extremely kind and supportive of me, putting in the effort, and really doing his best as an advisor, which, I really do appreciate. As a bonus, he is relatively well published. Undoubtedly, a publication would be a good application item for me, perhaps helping me achieve more/better research opportunities as an undergraduate, and as such, further advancing my grad-school and academia aims. If it is relevant, the field is theoretical CS.
What should I do? Can this have negative effects on my future career?