"Community property" is a marital property term. Fences fall under the classification of a property fixture.
Depending on the accuracy of installation along the property line you may or may not have a shared fence with the neighbor. Interestingly enough, if the fence was truly placed on the property line you may be interested to know it is quite possible your Neighbor owes you some money as California Civil Code Section 841 states:
"Coterminous owners are mutually bound equally to maintain: 1. The boundaries and monuments between them; 2. The fences between them, unless one of them chooses to let his land lie without fencing; in which case, if he afterwards encloses it, he must refund to the other a just proportion of the value, at that time, of any division fence made by the latter."
[ http://law.onecle.com/california/civil/841.html ]
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No matter why you have asked your question, seek legal advice about your specific situation if you believe any neighbor may be unreasonable or just want to know what your specific rights are.
It is best if you talk to your neighbors if you want to take it down and tell them what you want to put up instead to improve it. If they do not agree stay with what is there!