A sequence in PostgreSQL does exactly the same as AUTOINCREMENT in MySQL. A sequence is more efficient than a uuid because it is 8 bytes instead of 16 for the uuid. You can use a uuid as a primary key, just like most any other data type.
However, I don’t see how this relates to the masking of a user ID. If you want to mask the ID of a certain user from other users, you should carefully manage the table privileges and/or hash the ID using – for instance – md5().
If you want to protect a table with user data from snooping hackers that are trying to guess other IDs, then the uuid type is an excellent choice. Package uuid-ossp has several flavours. The version 4 is then the best choice as it has 122 random bits (the other 6 are used for identification of the version). You can create a primary key like this:
id uuid PRIMARY KEY DEFAULT uuid_generate_v4()
and then you will never have to worry about it anymore.
PostgreSQL 13+
You can now use the built-in function gen_random_uuid() to get a version 4 random UUID.