It is not grease that lubricates. it is the oil which is suspended within the grease that lubricates.
I am led to believe that Lithium soap based grease is compatable with just about all lubricants, this may be the reason why it is specified.
Google is your friend
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A grease (lubricant) is a mixture of oil and a soap. The soaps are dispersed into and viscosify oils to form stable gels. Lithium grease adheres well to metal, is non-corrosive, may be used under heavy loads, and exhibits good temperature tolerance. It has a drip temperature of 190° to 220°C (350° to 400°F) and it resists moisture, so it is commonly used as lubricant in household products, such as electric garage doors, as well as in automotive applications, such as CV joints. Some formulations also include PTFE and/or other substances, such as molybdenum disulfide.
• Lithium soap thickened gear grease.
• Contains highly refined mineral oil, anti-oxidation & extreme pressure additives.
• Provides NLGI 00 consistency.
• Designed for high temperature & arduous loading conditions.
• Compatible with mineral gear oils.
• Designed for gearboxes that have operated satisfactorily on mineral oil, where main requirement is to extend both the lubricant service life & maintenance period.
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Whenever I fit an oil seal, I use a small quantity of the lubricant I intend to run to lubricate it.
As Civic says the grease is only going to be there briefly, until it is washed away.
If one really wants to be picky when installing the gear side seal, put the 2 stroke oil of your choice on the inner lip, and the transmission oil of your choice on the gearbox side.