In my opinion, you are in a situation where both rules govern. However, to be certain you would have to review the CC&Rs to see if they apply to your "community roads." I bet they do.
Those HOA rules can be more restrictive, e.g, the can prohibit parking on the community roads and can set a lower speed limit. I also believe they could prohibit the type of riding you mention.
If you do not like the proposed rule changes, seek a rule that is more accommodating -- become a participant in your HOA meetings and get other members to agree with your position. Good luck.
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While I don't practice in California and do not disagree with the previous answer, the question is are these public roads or are these private roads. It's easy to determine if you're in a gated community, but not so easy to determine otherwise. You need to carefully read the description of the commn areas in your community and see if the roads are part of what the community owns or if they are public. If they are public, the California rules of the road would apply. If not, the Association, acting through its board, usually has the right to create rules and regs for the use of the common areas. Please remember, roadways whether public or private are used for transportation by vehicles weighing tons and if a child on a bike darts out without looking, a car backing up or that can't see because the bike is in it's blind spot could inadvertently take a life. The rules may seem unreasonable on the part of the board, but it could also be a safety first issue.
This is not intended to be legal advice or create an attorney-client relationship. If more information is needed, you should consult with an attorney in your state regarding the specifics of your situation and the options available to you.