Reinitializing Subscription Performance I have 4 Servers, Servers A, B, C, D.

Server A publishes a Replication instance, and Servers B, C, D have Pull Subscriptions to it.

Server B's subscription needs to be Reinitialized, but I am concerned that reinitializing it (Using the "current snapshot", not by generating a new one) will impact Replication Performance to the other Servers.

Should I be concerned, or because Servers B, C, and D have Pull (instead of Push) subscriptions, am I just over-thinking this?
It really depends on how old the snapshot is.  After the snapshot is applied, the agent will need to also send all of the changes that have occurred since the snapshot was taken.  Depending on how many changes have occurred, this may or may not affect other existing subscribers.

I tend to take a new snapshot if possible before reinitializing a subscriber although sometimes that is not an option.

I wouldn't worry too much about it impacting other subscribers.