I'm guessing that police tape was for something more sinister than trail bikes. On the topic of rules and restrictions, public land managers fear legal exposure, so it probably depends on local circumstances as to whether speed limits or other limitations on bicycles could be contemplated. What is definite is that there will be increasing competition for land access and vested interest groups will leverage against cyclists if it suits their cause. Unlike the US, Qld and NSW national parks services have released policy documents officially supporting MTB. That at least gives us a head start, but it also means that in the future MTB in national parks can be officially controlled. It is how that happens that is a bit unpredictable.
Our local national park - Nerang on the Gold Coast, is riddled with trail. Some years ago a trail survey was conducted and most of those trails were designated as MTB trail not yet of a standard suitable for signposting. Sounds like progress. They gave the trails to the MTB community and entrusted us to bring the trails up to standard. What they didn't do was take ownership and responsibility for their assets. For that reason there is no public map of the trail system and almost no trails are signposted. IMO that was for 2 reasons - first they don't have the staff or money to bring those trails up to their standard (whatever that is, but based on the old IMBA standards) and secondly because the local staff really don't support MTB access. The second may be changing but I reckon if we didn't have the Commonwealth Games coming up, there would be no support at all from the local land manager. Putting you head in the sand so you cannot see that there is a MTB trail system seems to be the main strategy of our land manager.
When a trail is not signposted it has no identifiable designation to the public. That means horse riders argue it is shared trail and get really fucking nasty when you question their presence. No rider wants trail damage or conflict with horses and I get sick of the 2 types of horseshit they leave in the park, the kind that come from a horses' back end and that from their owners front end. "We can go anywhere we like. The trail is not just for you you selfish dickhead. etc". Trouble is that while they are wrong, if there is no sign then they could conceivably argue that it is shared trail. I fear that in court an injured equestrian will argue successfully that they were not in the wrong place and because a cyclist did not yield to their horse (something that is on the limited number of signs in the park), then that cyclist will be in the wrong and will get zero support from the land manager. Further to that, after many years and thousands of hours of volunteer trailcare, I fear that the land manager will also not support the trail crew who worked on bringing that trail up to standard and negligently failed to provide trail that was safe for all users, even if there was only supposed to be one user group - MTB. End result is that after failing to see any commonsense over the issue of trail use and standard, I will no longer work on our trails (other than basically clearing trails of loose or fallen obstacles). I have enough liability in my life and need no more.
How does all this relate to other regs and speed - well, it means that anything could happen and we, the MTB public will have little or no say in it.