The Supreme Court has posted its schedule of oral arguments for the rest of this term--which concludes in July--without any reference to two controversial cases, the denial of tax exemptions to two racially segregated private schools and the legal fate of the Equal Rights Amendment.

In the ERA case, the failure to schedule apparently means that the court will not consider the issue until expiration of the June 30 deadline for final ratification of the amendment by the states.

The case before the court involves an Idaho judge's ruling that Congress' 1978 extension of the ratification deadline was illegal, and that states could therefore rescind their approval.

In the tax exemption case, the effect is less clear and has become a favorite subject of speculation by court watchers and lawyers. While it is possible that the court will put off oral arguments until the fall, several observers believe the court might take the unusual step of deciding it without formal argument.

Bob Jones University, of Greenville, S.C., and Goldsboro (N.C.) Christian Schools Inc. are challenging the Internal Revenue Service's ruling that they are not entitled to tax exemptions because they discriminate against blacks.

The Reagan administration created a furor early this year when it reversed the government's longstanding position denying the exemptions and told the court the case should be dismissed as moot because the IRS would grant tax-exempt status.

After a court of appeals blocked granting the exemptions, the government told the court the case should be heard after all. But it took the unusual step of asking that another party defend the original IRS position.

William G. McNairy, Goldsboro's attorney, said in a telephone interview yesterday from Greensboro that he feels the court is writing an opinion without arguments because the case has been on the court's Friday conference calendar for several weeks without appointment of a third party to defend IRS.

Philip J. Murren, one of the Bob Jones University lawyers, said yesterday he would not speculate about the court's actions because "I don't know of any case that comes close to this one in being unusual."

Because the government has changed its legal position since arguing last fall that the court hear the case, the justices could change their minds, too, and decide not to rule at all. That would have the effect of upholding the 4th U.S. Circuit Court of Appeals decision against the schools.

One government lawyer noted that holding the case over until the fall would force the administration to argue its new position in support of the discriminatory schools just before the November congressional elections.