Q:

Could you actually make a green space program?

Is it plausible to build and maintain a space program without adding to climate change?
While obviously there are larger problems in the near term with respect to climate change, I'm thinking about a slightly longer term context with something like solarpunk. If we could reasonably have clean energy dominate(and I understand that is a big if), could we still keep a space program going?
I actually think the real problem might be economics. Assuming an eco-energy future, this implies that there would probably be a lower overall standard of living than we currently see in the US, which means there would be less resources to spend on something like a space program.

A:

We could do it tomorrow if we wanted to
We don't because it's cheaper to do things wastefully than green.
Now it's usually cheaper not because being green is implicitly more expensive, but because of subsidies for oil and gas companies, which run into the billions of USD per year, and that they're more established and have economies of scale. If the government decides to quit oil and gas and go green, the space program could survive and, after retooling, thrive even.
The biggest cost will be in 2 areas: manufacturing space craft, and getting those space craft to orbit. Everything else I'm assuming can be covered by "put some solar panels on the roof" or "buy local" level of greenness, same as any other office or government department.
Making space craft green
Steel and Aluminium are very energy intensive to make, but that energy can come from a green source, Eg Germany is making green aluminium, or be offset by carbon credits. Also a focus on the re-use of ships (eg SpaceX's auto landing rockets) helps spread this environmental cost over the life of the rocket.
Many parts like plastic on the rockets are theoretically recyclable, or derivable from a green source, just it's not ecconomically viable to do so. When your government starts limiting the amount of oil which can be extracted to the point that prices of oil-derived products start to rise, we'll switch to green substitutes as soon as they become cheaper. PLA plastic is a pretty good example, it's common for entry-level 3D printing, that's derived from corn. Any exceptions (rare metals in computers, for example) can be covered with carbon credits.
Fuelling them greenly
You just need a lot of energy to get to orbit, that energy needs to come from somewhere, but where that comes from can be green.
How much fuel is needed to launch a rocket varies between designs, and I can't find consistent figures (and they're in freedom units rather than metric), but this link says 390 kilogallons of H2 and 145kilogallons of o2 in the external tank. Factoring in the shuttle internal fuel tanks hold fuel too, and the effect of the solid fuel boosters helping at the start, I'm guessing 500:200kilogallons of liquid hydrogen/oxygen should do the trick to get a decent sized rocket to LEO.

500 kgallon liquid h2 weighs 130 metric tonnes. (http://www.uigi.com/h2_conv.html)
200 kgallon liquid o2 weighs 860 metric tonnes. (http://www.uigi.com/o2_conv.html)

To produce 1kg of hydrogen by electrolysis costs about 50kWh, and you get the oxygen included it that. Excluding pressurisation and refrigeration costs, you're looking at 6.500TWh of energy per space launch.
The emissions put out by burning liquid oxygen and liquid hydrogen is - water vapour. It's the ultimate green fuel!
So how often can we launch?
Current solar production (as of 2018) in the USA is 96.1TWh. Using only existing solar installations in the USA, you could do 14 launches a year.
If the solar output of china (204,700MW) was channeled entirely into fuel production for space craft launches, they could launch an equivalent rocket every 31.8 hours of direct sunlight. In summer the Chinese could maintain 3 launches per week entirely on green fuel, on their existing solar networks. (And 2 per week in winter)
The entire planet has a green energy production output of 2.3TW (combining hydro, solar, and wind) If the world unites, we could launch a rocket on green power every 3 hours of full power generation.

