Rod, technically, words such as anyone, everybody, nobody and one are singular, so some - including you, apparently - claim they should not be followed by plural forms such as they, them and their. However, this �rule' has been consistently flouted for centuries by quality writers using such phrases as "Nobody in their senses would..." rather than "Nobody in his senses would..." or - even worse - "Nobody in his or her senses would..."
This is because the idea of plurality is actually contained in these indefinite pronouns. It also gets around the problem that there is no genderless way of referring simply to both male and female persons in such structures. If we did not use "their", we would be obliged constantly to say "his or her", which is clumsy. These pluralised forms are here to stay and regarded as perfectly acceptable now.