Rinse meat after marinating in yogurt?
Don't Rinse

You should not need to do more than shake the excess marinade from your chicken, or if you want to be very thorough, pat it down with towels lightly.

If you rinsed, you would be washing away from of the flavor developed by your marinade, and the seasoning at the surface of the chicken.

Cook on

The goal is to not put the chicken on the grill with so much left over marinade that it fails to cook through and dry.  By the time you are done grilling, the chicken should be essentially dry at the surface with nothing left to curdle.

The other goal of the grilling (or putting in the tandoor, I imagine, if you have one) is to develop the nice browned and delicious flavors, and that won't happen if there is still liquid yogurt on the surface.

Type of yogurt

The particular type of yogurt you use should not be a factor, since it should be fully cooked in the grilling phase.

However, in general, very high fat dairly products (like cream, or a yogurt made from full cream).