No, the filter is not safe!
No filter is "safe," if you fear health effects then do not use the filter. Please do not use a mask's article or talk page to discuss the safety of a filter.
The GP-5 filter canister is a Soviet-made 40mm (GOST thread) combination NBC filter issued for civil defence purposes. Introduced during the 1960s, the filter, issued in the GP-5 kit, was mass manufactured, and is the most common filter in the world at present.
GP-5 filters come in a olive-drab colored canister with a screw-on cap whose color varies on what batch the filter is. It features exterior markings that show the filter model, batch and year of manufacture and other markings on the top, bottom and on the inlet aperture itself. The filter weighs average and the canister, being metal, is prone to dents and scratches. The filter uses a particulate filter for aerosols, smoke and viruses and has a carbon bed for vapors and other chemicals. The carbon bed appears to be inside a cotton enclosure. The contents are held by a metallic frame inside the canister.
Lab reports from the Netherlands and Finland have confirmed the presence of asbestos in the GP-5 filter, in both the particulate filter, and the activated carbon (likely due to contamination), in filters produced up to at least 1988, with use in subsequent years seeming certain. 
The GP-5 Filter, despite its age and content, is still being sold around the world and many distributors stock them as entry-level filters.