It’s completely normal to go to the theatre by yourself and I often do, it’s hardly ever noticed. I work in the theatre industry and as part of work many of us go alone, for example;
The director, choreographer, writer, producer of the show or anyone else involved with the production may want to watch the show to see how the run is going and how it can or needs to be improved upon.
Critics/Reviewers will most likely be alone when they watch a production.
Actors who are about to replace a current cast member when their contract ends will often watch a show alone to get a broad overview of how the show runs and what their place in it will be.
Casting directors and agents spend several nights at the theatre per week. They may go with other casting directors but I’ve almost always seen them there alone unless it’s Press Night.
Students, academics, researchers etc will often go and watch shows alone.
So there you are, it’s a normal part of life for many people and that’s before you get men and women who just like to go alone anyway, of which there are many!
Go for it and enjoy!