Yes, clan temples are almost exclusively for use by the clan. You might visit, but you would be a vistor. You don't have the assumed right to learn spells at an Orlanth temple in your neighbouring clan, even if in same tribe. Clan temples, especially to long-established clans like the Haraborn, quite often teach spells available nowhere else.
Cults of Runequest: Tribes
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Yes, clan temples are almost exclusively for use by the clan. You might visit, but you would be a vistor. You don't have the assumed right to learn spells at an Orlanth temple in your neighbouring clan, even if in same tribe. Clan temples, especially to long-established clans like the Haraborn, quite often teach spells available nowhere else.