People often stick to their existing beliefs, ignoring contradicting evidence or only interacting with those who reinforce their views. Social media platforms often facilitate such tendencies of homophily and echo-chambers as they promote highly personalized content to maximize user engagement. However, increased belief rigidity can negatively affect real-world policy decisions such as leading to climate change inaction and increased vaccine hesitancy. To understand and effectively tackle belief rigidity on online social networks, designing and evaluating various intervention strategies is crucial, and increasing randomization in the network can be considered one such intervention. In this paper, we empirically quantify the effects of a randomized social network structure on belief rigidity, specifically examining the potential benefits of introducing randomness into the network. We show that individuals' beliefs are positively influenced by peer opinions, regardless of whether those opinions are similar to or differ from their own by passively sensing belief rigidity through our experimental framework. Moreover, people incorporate a slightly higher variety of different peers (based on their opinions) into their networks when the recommendation algorithm provides them with diverse content, compared to when it provides them with similar content. Our results indicate that in some cases, there might be benefits to randomization, providing empirical evidence that a more randomized network could be a feasible way of helping people get out of their echo-chambers. Our findings have broader implications in computing and platform design of social media, and can help combat overly rigid beliefs in online social networks.