Open Space Protection Act of 1998 - Amends the Land and Water Conservation Act of 1965 to appropriate from the Land and Water Conservation Fund $900 million for every fiscal year from FY 1999 through 2015, with specified portions available for:  (1) Federal purposes (Federal share); (2) financial assistance to the States for State and local natural areas, open space, parklands, or recreational areas; (3) grants to local governments through the Urban Parks and Recreation Recovery Program; (4) grants (through FY 2004) for land acquisition in connection with the American Battlefield Protection Program; and (5) grants (for FY 2004 through 2014) for the restoration and acquisition of historical and cultural sites found within the National Park Service, Fish and Wildlife Service, Bureau of Land Management and the National Forest Service. 
(Sec. 3) Requires the President to:  (1) require the Secretary of the Interior and the Secretary of Agriculture to prepare Federal priority lists for expenditure of the Federal share; and (2) name in the annual budget submission the specific purposes for which the Secretaries shall use such funds, unless Congress specifies otherwise. 
(Sec. 4) Requires Indian-Alaska Native Village Corporations to be treated as one State for allocation purposes. 
Authorizes the Secretary to approve conversion of property improved or developed with Federal assistance to other than public recreation uses only if the State demonstrates no prudent or feasible alternative exists (with the exception of those properties that are no longer viable as an outdoor conservation and recreation facility due to changes in demographics, or that must be abandoned because of environmental contamination endangering public health and safety).  Requires any conversion to satisfy any conditions the Secretary deems necessary to assure the substitution of other conservation and recreation properties which are:  (1) of at least equal market value and reasonably equivalent usefulness and location; and (2) in accord with the existing State Plan for Conservation and Recreation. 
Declares that wetland areas and interests identified in the action agenda, and proposed for acquisition as suitable replacement property (acceptable to the Secretary) within that same State, shall be considered to be of reasonably equivalent usefulness with the property proposed for conversion. 
(Sec. 5) Amends the Urban Park and Recreation Recovery Act to include in the list of local governments eligible to compete for Federal assistance grants for the Urban Park and Recreation Recovery Program:  (1) all political subdivisions included in Metropolitan, Primary, or Consolidated Statistical Areas; (2) any other city or town within a Metropolitan Area with a total population of 50,000 or more in the 1970, 1980, 1990, or subsequent census; and (3) any other political subdivision, county, parish, or township with a total of 250,000 or more in the 1970, 1980, 1990, or subsequent census. 
Authorizes the Secretary of the Interior to make to local governments matching capital:  (1) development grants to cover costs of development and construction on existing or new neighborhood recreation sites, including indoor and outdoor recreation facilities, support facilities, and landscaping (but not routine maintenance and upkeep activities); and (2) acquisition grants to cover the direct and incidental costs of purchasing new parkland to be permanently dedicated and made accessible for public conservation and recreation. 
Authorizes the Secretary to approve conversion of property improved or developed with Federal assistance to other than public recreation uses only if the grantee demonstrates no prudent or feasible alternative exists (with the exception of those properties that are no longer a viable recreation facility due to changes in demographics or that must be abandoned because of environmental contamination endangering public health and safety).  Requires any conversion to satisfy any conditions the Secretary deems necessary to assure the substitution of other conservation and recreation properties which are:  (1) of at least equal market value and reasonably equivalent usefulness and location; and (2) in accord with the current conservation and recreation recovery action program. 
Repeals the prohibition against using funds under such Act to acquire land or interests in land.
Output: Open Space Protection Act of 1998