How to review a revised paper I have already rejected? I reviewed a manuscript submitted to a high-impact journal. The quality was low and I believed it could not reach the journal’s standards even by revision. I clearly recommended rejection.

Now I received the revised version for review. Two of three reviewers (myself included) had suggested to reject the original paper. The third reviewer suggested a major revision. Nonetheless, the editor had asked the authors to revise the manuscript (I never experienced this before).

Clearly, the editor is in favor of publishing this paper (for personal or professional reasons; I cannot judge). What should I do? I publish 80% of my works in this journal, and it is very important for me to avoid any conflict with the editor.
When you recommended rejection, you presumably listed a series of issues that made it unacceptable.  On the revision, you go back and repeat the list of issues and simply say for each one, "The revision has/has not corrected this problem".  If you reach the end of your list and all the issues have been corrected and no new issues have been introduced in the revision, then you say the paper is now suitable for publication. If the issues have not all been corrected, then you say "The paper is still not suitable for publication because the issues I noted previously have not been corrected."