It means to “follow one’s favorite activity.” No sexual connotations.

One source.

Are you familiar with hobby horses? If not, here is one example and here is another.

“Riding the hobby horse” can mean something sexual, but without more information on how the phrase was presented, it’s difficult to guess the context. Here is the “Urban Dictionary’s list of meanings.

It means your strong interest or obsession.

For example, if a politician pushed for years to build a new airport or sports stadium, the press might say it was his “personal hobby horse”.

For me “riding the hobby horse” means really riding the hobby horses here at the ranch.
I also shovel a lot of hobby horse shit. lol

For me, a hobby horse is the same as a rocking horse. You can ride it all day, and ride the hell out of it, but you don’t get anywhere.
Also, you ride the hell out of it as if it were a real horse, but it isn’t real. It’s pretend.

[NSFW] could it be one of these?

Probably means liking an activity or some really weird sex.

I have always thought this was simply about sexual intercourse, along the lines of “taking the pigskin bus to tuna town”, but it appears that there are implications of promiscuity and/or prostitution attached to it and that it has some history including a reference by Shakespeare in A Winters Tale : “My wife’s a hobby-horse, deserves a name as rank as any flax-wench that puts to before her troth-plight: say’t and justify’t.”

‘Riding the hobby horse’ probably means to always use “a topic to which one constantly reverts.*”
*-from Merriam-Webster’s Collegiate Dictionary, 11th ed.

So far, most of everything I have read is completely incorrect (the answers that I have seen here). I have often thought of what the expression means. It is used in the movie “Inherit the Wind” with Spencer Tracy and Frederick March. There is a scene where (in the courtroom—they are both lawyers) Spencer Tracy is apologizing to the judge for things he said the day before. It is then that Frederick March comments (about Tracy): “He is well known to have ridden hobby horses before.”