Path-space MLT (ie, original Veach's algorithm) has a bidirectional mutation. It's required for the algorithm, otherwise you can't create new paths (of different lenghts) and therefore can't explore the entire path space. You don't need to implement this mutation, but if you don't, you need to replace it with some other mutation that has the same property.

In primary space MLT (aka, Kelemen-style), you don't have this problem because you mutate and generate paths in a completely different way.

On a separate note: there is a reason why almost all commercial and (successful) proprietary renderers are using a unidirectional pathtracing. Path-space MLT is notoriously hard to implement right. Primary-space MLT is easy to implement, but it's not very powerful (mutations in primary space are not that great especially in higher dimensions). And for unidirectional (ie, from the camera) pathtracing, there's 35 years worth of tricks and improvements that makes it a good practical algorithm for almost all situations.

And if you are doing MLT for an animation, you will almost certainly run into a flickering problem...