It depends on the use case, for example user streams would work with different user tokens, but the public sample and filter endpoints are not intended for multiple connections.
If you repeatedly try to connect to the streaming API too quickly, or with too many streams per IP address, then this throttling can occur. For simple, occasional one-off or single continuous stream connections then it should be fine.
The streaming API is not designed for large volume, multiple connections for many users on a single IP basis. The deprecated site streams API (which is being removed) was an initial attempt at that, but it is now being replaced with the account activity API which is webhook-based.
If you require larger volumes of data then the commercial Gnip APIs are available.