Do you?

When two persons you respect disrespecting each other,
do you stop respecting either one?

After I let the thought brew for a few days, it seems to me that you can't help it: You will (involuntarily) stop respecting one of them because there will be one of them that you respect more.

They don't even have to disrespect each other; the doubt can come even when only one of them dislike the other one. In this case, I think you would start disrespecting the person who shows dislike the first.
For example, we respect both Yoda and Anakin, but when Anakin start disrespecting Yoda, of course the natural thing that would happen is we lose our respect to Anakin.

That is just a gist, the fact is definitely a lot more complicated than that.