In science we have a means to discover facts about the world and to share those facts with others. Others can follow the same specific method and should see similar results in a comparable range. It isn't going to be perfect, because you cannot always account for every confounding variable or predict what slightly altered conditions will produce, but that scientists account for this as a group is also evidence of group recognition of sources of bias.Well, you asked for a more reasoned challange.
Now remember I am not a metaphyiscal supernaturalist and all the rest. For the purpose of this, I am a skeptic.
The bold one is all I need, because in effect the question is if all learning about the world can be done objectively. That is where it ends in practice for actual scientism.
Now in my culture there are 7 variants of science and the hard one from your culture is not the only one.
In short there are your exchanges as you are engaged in them and then there are if science needs to be only about that which can be tested objectively, observed objectively and reasoned about objectively.
Or if you can include a limited version of subjectivity.
That may approximate objectivity as well as can be done. Subjectivity and bias is always going to be there.
I'm still trying to figure out where you are going with this, but it sounds interesting.