Swift: ‘Hashable.hashValue’ is deprecated as a protocol requirement;

As the warning says, now you should implement the hash(into:) function instead.

func hash(into hasher: inout Hasher) {
    switch self {
    case .mention: hasher.combine(-1)
    case .hashtag: hasher.combine(-2)
    case .url: hasher.combine(-3)
    case .custom(let regex): hasher.combine(regex) // assuming regex is a string, that already conforms to hashable
    }
}

It would be even better (in case of enums and struct) to remove the custom hash(into:) implementation (unless you need a specific implementation) as the compiler will automatically synthesize it for you.

Just make your enum conforming to it:

public enum ActiveType: Hashable {
    case mention
    case hashtag
    case url
    case custom(pattern: String)

    var pattern: String {
        switch self {
        case .mention: return RegexParser.mentionPattern
        case .hashtag: return RegexParser.hashtagPattern
        case .url: return RegexParser.urlPattern
        case .custom(let regex): return regex
        }
    }
}