I assume you are using NeoPixels (WS2812) or something similar? These addressable RGB LEDs have a driver chips built-in. They just need a "little" (low power) data connection from the Arduino (and a common ground) and that can be shared.
I've never tried it but I'd expect you could drive many-many more... The datasheet lists input current at 1 microamp and the Arduino can put-out up-to 40 milliamps.
Input capacitance isn't specified and that could be the limiting factor, but I'd guess you can control more than 4 strips.
You could also just run 7 * 25 = 175 LEDs on one strip and take care in software to just duplicate the pattern of the first 25 to subsequent groups of 25.
There is no advantage to running 7 pins to 7 strips unless you have a time issue and would need to update only a small strip of 25. Updating 175 LEDs should still allow a decent frame rate for any effects you program.
The real advantage to not sharing 1 data to 7 strips is the gain in flexibility, as has been observed.