Is it fair to ask about citizenship on the census?

The census is used to determine funding for local schools. But all money, for all entitlement services is affected by how many people are living in the state, with some differences for non-citizens, so yes, it is very fair to ask.

Census data are used to determine how much federal funding is sent to the states, and then distributed to cities and towns by the states. The census is used by the federal government to determine the states per capita income as well.

Per capita income affects how much money the government will give the state for Medicaid programs, as one example, or for food stamps. It affects all the entitlement programs, such as Section 8 housing, and special education grants.

At age 65, or if disabled, Non citizens are not eligible to receive free part A Medicare, and they must purchase part B medicare.

Right now, benefit availability for non-citizens is as follows:

"Refugees and asylees are eligible for food stamps/SNAP.
 Refugees and asylees are eligible for SSI benefits and Medicaid for
seven years after arrival and are eligible for TANF for five years.8 After
this term, they generally are ineligible for SSI, but may be eligible, at
state option, for Medicaid and TANF.9
 LPRs with a substantial work history—generally 10 years (40 quarters)
of work documented by Social Security or other employment records—
or a military connection (active duty military personnel, veterans, and
their families) are eligible for the full range of programs.
 LPRs are not eligible for SSI during the first five years even if they had
40 credits of earnings (e.g., as a temporary worker prior to receiving LPR
status).10
 LPRs receiving SSI as of August 22, 1996, continue to be eligible for
SSI.
 Noncitizen SSI recipients are eligible for (and required to be covered
under) Medicaid.
 Disabled LPRs who were legal residents as of August 22, 1996, are
eligible for SSI.
 Disabled LPRs are eligible for SNAP.
11
 LPRs who were elderly (65+) and legal residents as of August 22, 1996,
are eligible for SNAP.
 LPRs who have been legal residents for five years or are children (under
18) are eligible for SNAP.
 LPRs entering after August 22, 1996, are barred from TANF and
Medicaid for five years, after which their coverage becomes a state
option.12 States have the option to cover LPRs who are children or who
are pregnant during the first five years"

https://fas.org/sgp/crs/misc/RL33809.pdf