Online social media represent an oftentimes unique source of information, and having access to reliable and unbiased content is crucial, especially during crises and contentious events. We study the spread of propaganda and misinformation that circulated on Facebook and Twitter during the first few months of the Russia-Ukraine conflict. By leveraging two large datasets of millions of social media posts, we estimate the prevalence of Russian propaganda and low-credibility content on the two platforms, describing temporal patterns and highlighting the disproportionate role played by superspreaders in amplifying unreliable content. We infer the political leaning of Facebook pages and Twitter users sharing propaganda and misinformation, and observe they tend to be more right-leaning than the average. By estimating the amount of content moderated by the two platforms, we show that only about 8-15% of the posts and tweets sharing links to Russian propaganda or untrustworthy sources were removed. Overall, our findings show that Facebook and Twitter are still vulnerable to abuse, especially during crises: we highlight the need to urgently address this issue to preserve the integrity of online conversations.