This study examines how engagement-maximizing recommender systems influence the visibility of Members of Parliament's tweets in timelines. Leveraging engagement predictive models and Twitter data, we evaluate various recommender systems. Our analysis reveals that prioritizing engagement decreases the ideological diversity of the audiences reached by Members of Parliament and increases the reach disparities between political groups. When evaluating the algorithmic amplification within the general population, engagement-based timelines confer greater advantages to mainstream right-wing parties compared to their left-wing counterparts. However, when considering users' individual political leanings, engagement-based timelines amplify ideologically aligned content. We stress the need for audits accounting for user characteristics when assessing the distortions introduced by personalization algorithms and advocate addressing online platform regulations by evaluating the metrics platforms aim to optimize, beyond the mere algorithmic implementation.