Can I participate in rural social security in Beijing with a Beijing residence permit?

Of course. According to official website, Beijing Municipal People's Government, 20211,Beijing Municipal Bureau of Human Resources and Social Security and Beijing Municipal Finance Bureau issued the Notice on Issues Concerning Foreigners' Permanent Resident Identity Cards and Hong Kong, Macao and Taiwan Residents' Residence Permits to Participate in the Basic Old-age Insurance for Urban and Rural Residents in Beijing. It is clear in the notice that those who live in Beijing but are not employed, who are over 16 years old and under 60 years old (excluding students at school), and who hold foreigners' permanent residence identity cards or Hong Kong, Macao and Taiwan residents' residence permits obtained in Beijing can participate in the basic old-age insurance for urban and rural residents in Beijing within the validity period. So you can participate in rural social security in Beijing with your Beijing residence permit.