Assuming I met him/her somehow:
I think it would depend excessively greatly on the context of how we met. I could see myself as being either extremely threatened by my clone (we both occupy the same niche in life, "there can only be one," what if she takes over my spot, etc.) but also feeling the desire to connect and join forces and explore the multiplayer parts of life/society that had been 'off limits' to me due to lack of a friend group whose thinking was more similar to my own. I definitely project in this case, since it's my clone: if I think s/he is a threat, isn't it likely that s/he feels the same way about me? Thus there is no way for me to be able to trust the other person, no matter how desperately I wish I could.
If they are a clone in every way (including gender, hobbies, interests, personality etc.) then that is the scenario in which I would be the least likely to get along with them. Of course, that would also be the scenario where I would most likely meet a clone in the first place. A clone with similar thought process but different/adjacent interests would still invoke the same anxiety and threatened feelings, but it wouldn't be overt and would possibly be manageable enough for me to consider them a 'frenemy.'
Most crucially there would need to be some believable reason for good will at the initial meeting. If our goals aligned and we had a reason to cooperate then great things could happen. If not.. then we'll hate each other. Hissing behind bars, wishing the other person would go away (but.. not actually doing anything to make them go away..). Just being miserable and further retreating into myself and pursuing competence in a mutual field in the hopes that I can one-up the clone enough for them to give up and go away, or at least alter their area of focus so that we're not stepping on each other's toes. In the latter case I think things would then settle into an uneasy truce of mutual respect.
Being both distant and quiet people I would find it incredibly hard to approach/speak to my clone, especially with so many fears just beneath the surface.