I understand and agree with you it's utter nonsense and bollocks how many places work on a default criteria being to work through a checklist and throw out any areas not met without going further.
Firstly I have worked with a breed specific rescue (border collies) which operates probably the most robust, thorough and complex process for re-homing which is often a source of frustration to some people however, those that take real exception to it typically expect to call up, get a dog and the rescue ought to be grateful for someone willing to take a dog off their hands.
The main criteria and biggest “rules” include not re homing dogs under 1 year old to ensure they have chance to be properly assessed for herding / working instinct, no homes where the dog will be routinely left for any length of time, no children under 12yrs and without securely fenced yards or gardens. They will however allow some leeway and play based on individual assessment of each person, every application and if someone doesn't have a yard or garden but fits the bill in other areas, they are willing to at least give more time and thought / follow up and find out more.
For example children under 12yrs is sometimes considered but only in exceptional circumstances i.e. it's a family owned and run farm. The overwhelming majority of dogs that are given up to them for re-homing have come from a family home where they had been bought as puppies intended to be a family pet and owners found themselves unable to cope with what often becomes a fully grown sheepdog in their home.
The breed is also one of the worst offenders in terms of nipping / biting young children typically due to herding instinct that need to be properly channelled and the dog live in a more suitable environment where they can be put to work.
That might mean an ideal home is found for a dog where they also have children under 12yrs so it's a case of assessing and considering everyone on merit.
The focus and rigidity of some centres almost allows people to re-home a dog, stick it outside a few times a day to sniff around and pee then bring it back in and consider that a suitable enough form of outdoor exercise. Someone looking for a dog that doesn't have a yard or garden like yourself can very often be the more suitable and if they have prior experience owning dogs, can provide details and satisfy staff they have more than adequate arrangements that's even better.
There shouldn't be any reason why someone is written out by default.
I live on a private road and our property opens up onto a dirt farm track leading across fields and down to the river. If we were to apply for rehoming a dog via some of the larger places, they wouldn't accept us or consider us point black because we don't have an actual yard or secure gated area. That we have a lifetime's experience owning dogs, train and work with a rescue centre to foster and help with rehabilitation prior to rehoming and three acres of land we rent is irrelevant. We don't have an actual gate so that makes us unsuitable.
No advice or anything to offer sadly but just to say don't let it totally dishearten you.