Contradiction on findings in existing literature I'm currently writing my thesis where I have two underlying sources where one says that a variable (has the founder of a kickstarter project backed other projects?) has influence on the dependent variable, while another source says it doesn't. What do I do in such a situation?
As Buffy notes, you cite both, and expound upon the apparent conflict.

If you are just reviewing literature, you would point out that the two studies came to different conclusions. If this is on-topic for your thesis, you would then dig a bit deeper and clarify what the studies have in common and how they differ, as it would lay out potential explanations for the apparent conflict.

This sort of thing is often the goal of reviewing literature to start with - identify a gap where there are no studies, or identify places where studies and/or theory seems to disagree.

Depending on what work you are doing, you may simply note this as a promising topic for future research, or you may want to try to address this conflict yourself with your own work to try to resolve the contradiction. The answer may be all kinds of things, from seeking out a mediating variable, to changing the analysis in a way that makes the conflict disappear, to ending up confirming that in fact "sometimes this variable matters, and sometimes it doesn't, and we don't know why."