It seems oversimplifying to say that robots are "just another worker." When women entered the workforce, they came with similar costs to their male counterparts; wanted breaks, expected time off, lunch break, commuting time, various facilities. Robots require...well, power. They don't need breaks or bathrooms, they don't even need to go home. Hell, if you really wanted to, you could run an entire auto plant with little/no climate control in complete darkness and the robots wouldn't mind one bit.
There's simply no competition between robots and humans, that's why I'm a firm believer that automation will take all the jobs and we need to figure out how to handle a post-work future before we start riots.