The cat cafe's business model is that there are cats which is comparable to Starbucks' business model in that they welcome dogs. The mere fact that they sell a drink aimed at dogs tells you their business model includes attracting dog owner's custom.
The fact that there are more Starbucks than there are cat cafes would suggest that dogs are more popular therefore the business model is more viable/profitable. If you really cannot live without Starbucks there is always Uber Eats or takeout.
I don't know what to suggest for the trains. Write to the train company and request dog-free carriages, perhaps? If enough people do it, they will listen. I completely get that allergies suck. I'm allergic to all kinds of things, including grass pollen and I also like to breathe but I can't demand that people don't cut their lawns so I can be outside. It would be nice if I could but the world does not revolve around people allergic to grass pollen, unfortunately.
I love cats too so I do get peeved when I visit my sister in the city and everyone goes to the cat cafe without me. I'd love to be surrounded by cats but, sadly, all the Piriton, optrex, ventolin, and Symbicort in the world wouldn't make that possible.
Dogs literally evolved with us, to be with us. Some scientists believe they actually assisted us in our own evolution. They are a very important part of our history. We are not going to suddenly stop keeping them as companions and as long as more people who like dogs continue spending their money businesses will continue to cater for them. It sucks for allergy sufferers. You have my sympathy but it is what it is and judging dog owners because of choices business owners made is not going to change that.
Like I said, if you think a dog-free eaterie would do well in your area, open one. I personally would love to open a dog cafe and have different rescue dogs attend each day but I can't afford it nor do I think it would be viable as a business. Dogs, unlike cats, tend to need a high ratio of handler to dog. The overheads would be massive on handler wages alone.
And if you think dog owners are in a minority stop spending at Starbucks et al and encourage others to do the same. Once they start losing money they'll change their business model. I strongly believe dog lovers are the majority, however. Like I said, we literally evolved together. We evolved to be dog lovers.