Is this service kit compatible with the MS 181 chainsaw?

No, this kit is not suitable for your MS 181 Chainsaw. Here are the comparable parts that are suited to your machine: Air Filter (With Fleece) - 1139 120 1602 Air Filter (Without Fleece) - 1139 120 1601 Fuel Pick-up Filter - 0000 350 3500 NGK Spark Plug - CMR6H