No problem.

Arguably it had something to do with Britain's class system being so heavily dominated by the aristocratic class. That created space for even some reasonably wealthy, middle-class and beyond people (particularly scholars, writers, educators, doctors, occassionally clergy etc rather than industrialists for example) to recognise a top down society that they also viewed as repressive to them at some level. Similar overlapping interests helped it gain solidarity with the suffragette movement for example, which included committed communists and anarchists, but nonetheless also had its fair share of liberals and even fascists.

It's also probably worth keeping in mind that the early and argueably most directly influential years of the Fabian society and movement predated even the October revolution in 1917, never mind the Chinese communist revolution in '27, so there was a lot of 'socialism in theory' going on. By the '30s Fabians were leaving (or being pushed out) right and left for their support of Stalin in particular, but also AES states in general.