There is no Byelaw preventing you from putting your feet on the seats. There should be- it wouldn't be a difficult Byelaw to frame. But there isn't.
Merseyrail's interpretation of their own Byelaw is therefore suspect at best.
The two Byelaws they use to justify their enforcement on feet on seats are Byelaws 6.4 and 6.8:
6.4 No person shall soil any part of the railway
6.8 No person shall molest or wilfully interfere with the comfort or convenience of any person on the railway.
If you put shoes on the seats there is a reasonable argument that you have soiled the railway, even if your shoes were relatively clean. But you didn't have shoes on.
Ironically, 6.8 is the weaker Byelaw but the one they tend to use more: if nobody is sitting in the seat when you put your feet on them, how can you be said to have interfered with their comfort or convenience? My view is that this doesn't- can't- cover any hypothetical person who might sit on the seat later and might hypothetically be inconvenienced by a seat with scuff marks on it.
Merseyrail are, generally, not open to negotiation on this point though. Their view is very black and white, if you don't pay the settlement then they will prosecute you.
There have been cases where the Magistrates have agreed that the law hasn't been broken but there have also been cases where the Magistrates have agreed that the law has been broken. So what you do now is largely down to your appetite risk. If the DBS is important to you then the best way of making it go away is to pay the settlement.
Speaking as a different random member of the public, it definitely does bother me - and that’s why the only defensible positions are “all” or “nothing”.
This is where it all gets subjective though. Is a socked or bare foot more or less offensive if it is on the floor? If the issue is the smell, that's the same wherever it is. Is a socked or bare foot more or less offensive than someone sitting on a seat in a pair of those really skimpy Nike Pro shorts that barely cover the buttocks? Lots of things interfere with my comfort- people whistling and people eating with their mouths open, for starters- but they're not enforced.
There are signs everywhere on Merseyrail trains, I, and many others, wish the industry as a whole enforced this as well as Merseyrail.
I agree about the enforcement, but my opinion is that their own Byelaws don't actually support the stance they take. It is such an easy Byelaw to frame, too: don't put your feet (irrespective of the wearing of footwear) on the seat or the frame of the seat.
I find it odd that they're so determined to enforce this but can't be bothered to take the time to amend their Byelaws to reflect their stance.