I think the problem is that both cyclists and horse riders are advised that they should ride two a breast so that it forces traffic to slow down and wait for a clear bit of road, instead of squeezing past a single cyclist or rider. I have often wondered at the selfishness of this advice, and the fact that it will and has, caused tremendous resentment towards them.
Everybody should coexist, but be aware of the other person and be polite towards them, and the fact that cyclists and horse riders pay no tax or insurance is just a red herring, to ensure that car drivers are more justified in their criticsim. Sadly this is not the case, but I feel it is up to all of us to be patient with other road users, no matter who they are - even old folk trundling along the middle of the lane on electric scooters!