When can the government use its own dollars to affect expression
 in a non-content neutral way?

1.  Under the Spending Clause, Congress cannot use its spending power to "induce the recepient to engage in unconstitutional activity"  (South Dakota v Dole).  Thus, if the Congress conditions a grant of money on the recipient taking some action that would violate the First Amendment rights of others, the action of Congress would be unconstitutional.  (Note: In U. S. v American Library Ass'n, dissenting justices Ginsburg and Souter argued that this principle was violated when Congress conditioned the grant of money to public libraries on the libraries using filters to block computer access to materials harmful to minors.)

2.  The government cannnot use its dollars to promote favored speech (or restrict unfavored speech) when the speech is not "a governmental message" made as part of a government program (Legal Services Corporation v Velazquez). The use of dollars to promote favored speech is permissible, however, when the speakers are participants in a government program and are, therefore, "government speakers" (Rust v Sullivan).

3.  The government cannot use its dollars to promote a particular viewpoint that is not related to a significant and legitimate government objective in the field of education (Board of Education v Pico). Legitimate and significant objectives, in the case of a junior high school library might include not exposing students to graphically sexual materials,  materials that condone drug use or violence, or materials that undermine educational objectives  (Pico). (Question: Is this still good law after Pleasant Grove?)

4.  When a government decision or action can be characterized as "government speech," it is "not subject to the Free Speech Clause."  Any limitation on the decision or action must come from another provision of the Constitution, such as the Establishment Clause (e.g., if the government speech promoted a religious viewpoint) or the Equal Protection Clause (e.g., if the government speech were to be aimed at harming a suspect class of citizens). (Pleasant Grove v Summum).

Use of government dollars page