I think the best cooperation is in terms of emergency rescue, backup communications, and sharing scientific results.
Emergency rescues mean compatible docking systems to that if an opportunity arises technical problems don't stop the rescue. Of course actually catching something in space in time to pull off a rescue is nearly impossible, but just in case the orbits line up...
Emergency rescue also means that moon/mars missions should plan to land ~10km from each other - while the area of exploration is greatly limited it means in the worst case you can walk to the other for safety. It also means a party in the middle one day - moral is itself an emergency.
Backup communication means that radio frequencies are compatible. That way "our relay can't reach our rover" can turn to "but we can - let us control it".
with diminishing returns. Post-Apollo funding was/is but a shadow of NASA's glory days. As soon as the military interest is gone, it's inevitable that a program will lose financial support.
Let's see. From the start of Space Age, October 4th, 1957, to the peak of NASA funding in 1966 - almost 9 years. To the last Apollo flight to the Moon in 1972 - a bit over 15 years. Advancements: unmanned space flight, manned LEO flight, manned flight to the Moon and back (overall manned flights ~43, https://en.wikipedia.org/wiki/List_of_human_spaceflights ).
From the Apollo Soyuz Test Project in 1975 to today in 2019 - 44 years. 3 times as much. Advancements: expanded unmanned space flight, permanent manned LEO outpost, reuseable vehicles (Gemini, STS, TKS, EB, X-37), commercial space flight, international space cooperation (overall manned flights ~270).
Per dollar modern space flights are quite competitive with 1970-s. Manned spaceflight is also safer than it used to be. Per unit of time... Mars flights are quite more robust, but Venus is kinda forgotten. Outer Solar system objects are visited more frequently... Russia retracted from unmanned spaceflight... India, China, Europe are growing...
I don't think funding is the only criteria here. In some aspects Apollo project catapulted humanity to the higher frontiers which are hard to keep, but some other indicators point to steady progress everywhere with way more sustainable longer term approach.
With China's ICBMs, aren't they already advanced enough that collaborating on space exploration with NASA won't teach them much ICBM technology that they don't already know?
I think we should share our discoveries and knowledge, but we shouldn't be partnering. If we really want space exploration, competition is what is going to drive it.