Do Cims avoid/not like transferring transport types?

Cims will walk a cumulative maximum of 128 units (1024 meters) per one-way trip. That includes walking to a stop, walking between stops, and walking from stop to destination. However, they will prefer any means of transportation if available, even for small distances (probably due to the fastest travel time algorithm ). Source: https://www.reddit.com/r/CitiesSkylines/comments/399rcl/seems_the_maximum_walking_distance_is_128u/

Transfers don't seem to count against the 128 unit limit, aside from whatever walking the cim has to do to make the transfer.

Regarding the limitation of the number of transfers, that should not be an issue for you if you are maxing at 3. In a very good mass transit network, every point should be reachable with at most two transfers, and ideally with at most one transfer. However, there are people that reported seeing cims make upwards of five transfers per trip.

Discussed also here: https://www.reddit.com/r/CitiesSkylines/comments/4dc8vf/transit_distances_and_transfers/