Answer
Does requesting a waiver reduce my chance of acceptance?
At publishers with a documented separation, no. Wiley states that editors of open access journals are not involved in APC correspondence. PeerJ says academic editors and reviewers are not made aware of a waiver request. Cambridge states the acceptance decision rests solely with editors. Where a publisher does not state this separation, it is not documented either way.
Detail
Where the separation is weaker
MDPI assesses waiver requests on the quality of the article as well as the authors' ability to pay, so the two questions are considered together by the managing editor rather than kept apart.