Hi Matt,
A definite "no" from me - I would not use car oil in a bike with a wet clutch. Bike oils have special friction modifiers designed to give smooth, reliable clutch take up - car engine oils, particularly synthetics are likely to result in contaminated clutch friction plates leading to jerky operation, or chronic slip.
Pay a little extra for a good quality oil of the right viscosity and avoid costly repair bills!
Best...
Andrew S
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