He enjoys proselytising his political views to his neighbors.

proselytising 是动词 proselytize 的现在分词形式。proselytize 来自名词 proselyte（皈依者、改变信仰者），加上动词后缀 -ize 构成，意思是"劝说他人改变信仰或观点"。在例句中指"积极宣传、劝说他人接受自己的政治观点"。