Time to get some rules into this discussion:
p.312
"When astrally perceiving, you become dual-natured (meaning you have presence in both the physical and astral planes simultaneously) and can interact with astral objects, including through combat."
p.315
"Astrally perceiving and dual-natured characters use their physical attributes and skills to fight opponents with a physical body, and their Astral Combat + Willpower to fight wholly astral entities. Astrally projecting characters use their mental attributes in place of physical ones (see Astral Attributes Table) along with the Astral Combat skill. There are no ranged weapons that function in astral space, so unarmed attacks, active weapon foci, and mana spells are the only options for astral combat."
p.394
"Whenever a critter flies, rends something with its claws, or paralyzes a target with a mere touch, it’s using a critter power. Powers are the special abilities that a critter possesses. Some critter powers are natural, such as their claws or tough skin.[...]
In order for a critter to use a power against a target, they have to be in the same state, either astral or physical. Astral forms cannot affect physical targets, and physical forms cannot affect astral targets (see The Astral World, p. 312). An astral critter that can materialize can affect physical targets if they do so, however, and dual-natured critters can interact with the astral plane as easily as the physical one."
"A dual-natured critter with a melee Natural Weapon can use this power against astral targets that are within its reach. Use the critter’s normal Unarmed Combat skill and physical Damage Value for this attack. Ranged Natural Weapons, like other ranged combat, do not work on the astral plane. Critters without a Natural Weapon may still make an unarmed attack. As with regular characters, the Damage Value is (STR)S. "
Ergo: It is possible to attack purely astral beings with your claws and fists as long as you are dual-natured.