I have always believed if you have a strong foundation in relational databases, know what normalization is and how to implement it, you can move from one relational database management system to another with minor learning curves. Granted they are all different in some way, some good and some bad, but the fundamentals are all the same.
I am not sure why some people only work in one flavor of database. Maybe their current employer only uses one brand? Maybe it is a personal preference? I personally go through stages. As an example, for the last year or so I have been working in SQL Server. Just recently I was moved to another project that is using Oracle as the back end.
Right now I do not like Oracle very much. Mainly due the fact my Oracle skills are on the rusty side and some of the things I did in SQL Server I can not do or must adjust to get to work in Oracle. Once things gear up and the cobwebs clear I will more than likely start to dislike SQL Server.
The majority of my career has been working in multiple databases, mainly MS SQL Server and Oracle by day and MySQL for projects I was doing on the side. I started using MySQL to broaden my knowledge and skill set and for the price tag.
In the past when I have been on the job market I looked for positions specifically for employers using at least MS SQL Server and Oracle. Sometimes it works out, sometimes not. It just so happens I currently work for a company where we use multiple brands of databases.
Keep learning and always try to do your best.