Hi OP, I know where you're coming from a bit because I had PTSD following a traumatic birth and one of my symptoms was that I became quite germ phobic (as part of the typical PTSD hypervigilance).
I was pretty horrified by soft play places, and it was only when DD started being invited to school friend's parties that we began going because I didn't want her to miss out.
The thing is OP, is that your germ phobia is just that - yours. It's not fair if your phobia has a big impact on your DS and means he misses out on things.
I don't mean to sound harsh, because I understand how all-consuming the anxiety can be, but the invitation really isn't about you, it's about your DS being included with his mates.
I know it's hard, your anxiety will probably really be spiking, but kids bloody love those places and have an absolute blast. The first time might be the worst for you, with subsequent visits being less stressful.
If you really can't face it then is there anyone else who could take your DS - on the basis of what the eye don't see, the heart don't grieve over.
If you do feel able to go, then try really hard to distract yourself - chat, read, enjoy seeing your son have fun.
I'm mostly over the germ phobia now, but still have an antibacterial wipe for any event in my bag. At soft play parties my DD and her friends line up for a wipe for their hands before they eat.
There's sensible hygiene practices and then there's a phobia that negatively impacts your life. OP, it's way off the OTT end of the spectrum to make your DS avoid using public toilets - you wouldn't want him to end up feeling anxious or upset about potential germs.
In the most sensitive way, have you considered perhaps talking to someone about your phobia? I'm not sure these things go away on their own and I'd be concerned the anxiety / avoidance behaviour would become more entrenched over time.
OP, do you know if there was a trigger/event that started your phobia?