It appears that you are a kind and empathetic parent, which is great, and is especially necessary in dealing with irrational fears.
You can't counter irrational fears with rationality. For example, telling a child that monsters don't exist will not decrease their fear of the monster they know is under their bed. You need to deal with their fears by validating the emotion, talking about their fear, gradual desensitization if the problem is amenable to this, and seeking solutions perhaps outside of the norm.
Validating their fears is not the same as agreeing with them; it simply means acknowledging that their fear is real. Try to find out if she experienced something traumatic (e.g. someone at preschool had an accident on the toilet and someone got mad), or what she thinks will happen if her urine touches a strange bowl or the pipes. Is there a toilet monster? Will it hurt her? Will the bowl or the pipes be angry/act up? Why is it threatening? Understanding her irrational fears will help you in your approach to the problem.
Desensitizing is time consuming; it's a chore. It would be a lot easier if, e.g., her fear was of dogs. But her fear is of toilets, so you kinda have to go there with her. Since she's not afraid of the toilet at home, this is more problematic. Do you still have her potty chair? Is it small enough to travel with? (There are some very portable travel potties.) What you do to help desensitize her depends on understanding why she's afraid. No reason is too silly; they're not silly to her. Perhaps you can go to a (clean) public restrooms at fast food restaurants or such where she can identify a threatening toilet. Have her use the potty, then dispose of her urine in the toilet together. If she's afraid of injury, note that the toilet (isn't angry/whatever her fear is.) Next perhaps you can have her use a strange toilet while you are there to protect her, holding her. Next, without you holding her (maybe just her hand.) Etc.
If this is not feasible, you can let her take the travel potty wherever she goes. If it's just to pee, she can pee in a paper cup (practice at home) and pour it into the toilet, wipe herself, and flush. Crumple the cup, throw it away, wash hands and it's done.
These are just suggestions; I'm sure you can come up with better ones when you know her specific fear. When she becomes more rational or her desire to be like everybody else is greater than her fear, she'll outgrow it.
Ideas to Help Reduce Your Child’s Fear and Anxiety
About Using the Toilet
I had a lot of irrational fears as a child, including the toilet monster. In my experience, to be told my fears were silly was not helpful. In my case, I think some of it was because I watched too many horror movies at a young age and I had a very active imagination; my older brother and sister went to a movie theater for a double feature - one of which was usually a horror movie - every week, and I tagged along. I saw all of the classics and then some on the big screen. And I still love a really scary show!
