Java 8 Stream Filter Map With Multiple condition

Why do you want to use filter here at all? The filter over stream of entries shown in the question iterates through all the members of the map ( O(n) ) However, the HashMap guarantees O(1) access to "get" functionality. So why sacrifice performance here?

If you want to check whether the map contains a key (ok, two keys), why not simply:

if("1".equals(hashMap.get("RED")) && "2".equals(hashMap.get("BLUE"))) {
   // yes, this map indeed contains both elements 
   // in case the "RED" is not in the map, the call to "get" will return null
}

Streams are not really appropriate for your problem. They are great for performing independent operations on members of a collection and then aggregating the results in some way. They are not great for functions on the collection as a whole or algorithms requiring interaction between members.

A much simpler formulation would be:

Objects.equals(map.get("RED"), "1") && Objects.equals(map.get("BLUE"), "2")

An alternative that avoids hardcoding the comparison would be:

Map<String, String> reference = Map.of("RED", "1", "BLUE", "2");

if (hashMap.entrySet().containsAll(reference.entrySet()) {
    ...
}

You can put both consitions in one filter itself

    Map<String, String> hashMap = new HashMap<>();
    hashMap.put("RED", "1");
    hashMap.put("BLUE", "2");
    hashMap.put("BLACK", "3");

    Map<String, String> filteredMap = hashMap.entrySet().stream()
            .filter(entry -> (entry.getKey().equals("RED") && entry.getValue().equals("1")
                    || (entry.getKey().equals("BLUE") && entry.getValue().equals("2"))))
            .collect(Collectors.toMap(map -> map.getKey(), map -> map.getValue()));
    System.out.println(filteredMap);