I would say that they are **harping on** about something (for whatever motive).

>If you say that someone **harps** on a subject, or harps on about it, you mean that they keep on talking about it in a way that other people find annoying.

[Collins][1]

[1]:https://www.collinsdictionary.com/dictionary/english/harp-on

>Trump began promoting Moore by **harping on** how bad it would be to have a Democratic senator in Alabama.

[Axios][2]
[2]:https://www.axios.com/3-how-trump-came-to-love-roy-moore-2516690256.html