Recursion per se isn't an issue; unbounded stack use is. If you either know your input size is bounded (e.g. it's not user-generated) or use tail-recursion (which should get compiled to a loop), it's fine.

If your algorithm does unbounded heap allocations instead, you're still going to get oomkilled. The actual vulnerability is not enforcing request resource limits. Things like xml bombs can then exacerbate this by expanding a highly compressed request (so a small amount of attacker work can generate a large amount of receiver work).