Hello! You have an excellent question. In fact, I think that it mainly affects two issues. The first relates to the formulation of the research question (eg, PICO, participants, intervention, comparison and outcomes) and the second to the minimization of biases related to the fidelity of your approach. If a trial is registered but not completed, it seems unlikely that you can get outcome data for your search query. In that case, such studies should not meet your eligibility criteria. However, some registered trials are completed but not published, in which case they belong to the "gray literature" and if they meet your eligibility criteria you should contact the authors and ask them to share their manuscript if possible. This way you minimize publication bias. Also note that some literature reviews aim to map the types of methodologies used in a given discipline or study phenomenon. In this case, it may be appropriate to include the recorded tests but specifying that they have not yet been published or completed. I hope my answer helps.
I agree with the comments made by Luc Dargis. If the objective of the review is to assess therapeutic efficacy and/or clinical safety through pooled data, it may be difficult to access relevant data from incomplete trials because it is still "work in progress" and not published. However, if you are conducting a study which is yet to be completed, and you have some data available with you, it may be included in the review citing it as your 'personal communication'. Needless to say, use of published data would lend more credibility to the review.
I usually search in database of ongoing studies. I think it is relevant, because you are saying for your reader that exist some additional information that might change the estimate of effect. I my case, I just cite the register numbers in the text, pointing that are ongoing studies . It is a way to broaden the search