I've been at this for a while but I think I've finally cracked the code on how to obtain open source US census images.
Unfortunately, it seems that census images taken from Family Search and Ancestry are governed by their license with the US government. You can download the images and use them for your own personal use but they forbid uploading and sharing on public websites. In other words, you shouldn't put them on profiles and free space pages.
Of course the "fair use" expception can be applied but to fit into the definition of fair use you can only include the information about the person or family you're covering. This means that a crop of a few lines on the census may be allowed but uploading the whole page is out.
If you want to upload the whole page, there is hope:
Archive.org has obtained the entirety of the census image database and they offer it on their website. You can find the census records here: https://archive.org/details/us_census
The problem is, and it is (was) a big problem, is that the images aren't searchable in their entirety and they seem to be uploaded in a random way so that all the states and counties are mixed up.
I've been playing around with the database for a while and I found that if you take the identifying information from Ancestry or Family Search, specifically the reel number, you can find the specific reel (about 700 pages) that your record will be in.
I tried searching the link above, scrolling down farther and farther, looking for my reel and there are thousands. The easiest thing to do is just grab one reel and then replace the reel number in the URL with the reel you are looking for.
For example, on the profile of Newton Walter Baty (1866 - 1953), there is a source for the 1880 census:
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MDLS-F15 : accessed 29 February 2016), Newton Baty in household of Saml H Baty, Knoxville, Marion, Iowa, United States; citing enumeration district ED 125, sheet 698C, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0354; FHL microfilm 1,254,354.
Going back to the Archive.org census page https://archive.org/details/us_census you will see the link for the 1880 census: https://archive.org/details/1880_census
Once you click on this link you will see several reel links:
Vol Reel 0943 - 1880 New York Federal Population
Vol Reel 1275 - 1880 Tennesee Federal
and so on.
Click on any of them, in this case, reel 0943 and you will be taken to this page:
Looking at the Family Search source above you can see that Newton's record was found on reel (roll) 0354. Just take the link above and replace 0943 with 0354:
Once I clicked on that link, I find that I'm at:
Reel 0354 - 1880 Iowa Federal Population Census Schedules - Mahaska (cont'd: ED 175, sheet 17-end)and Marion Counties
And this matches, as you cans see from the FS source above, we're looking for Marion County, Iowa.
Once you're inside the right reel, you can now search by name for your ancestor. So far, I have not had any luck with the search function. So I went looking for my page number. Scroll up to the top left of the image and find the page number and then go to the Archive reel and find the corresponding page number. Once you match the page numbers, you'll find your record and it is open source. You can share it to your heart's content.
Family search image for Newton Baty:
Archive.org search image for Newton Baty:
Hope that this is useful to a few folks. I welcome your comments and questions.