I have spikes on my floorstanders. I pierced them through thick berber carpet and pad by rocking them in place until they made contact with the concrete floor.
Next step is levelling.
I suspect the OP’s issue is that the spikes are glued in and not adjustable.
Spikes have to be adjusted so that the speaker is level and that all 4 make proper contact with the floor. Otherwise the speaker will be unstable regardless of carpet or no carpet.
OP- if you have access to an industrial heat gun you can heat the glue and when it softens use a set of vice grip to loosen the threads and remove them. Once they become adjustable again try to pierce through the carpet and then adjust for level and stability.