This is absolutely common that needs differ from client to client and that they want to drive the product in different directions.
There are three options for any given change:
1) You don't do it - they've bought product software, they have to live with the product. I wish Word did somethings different but I paid a couple of hundred pounds for it rather than having a bespoke word processor built from scratch so I have to live with it.
2) You branch the product and have two different versions - as often as not this is the worst thing to do. As a software house your model is dependent on many clients contributing to a common code base. Having multiple versions significantly increases costs (every bug fixed twice, two manuals, etc. etc.) and breaks your business model. Again, if they want bespoke software built exactly to their requirements then they need to pay for that - you don't get bespoke software at package prices.
3) Customisation (potentially as an option / module / configurable setting) - this can work but you really need to think about whether it's the right thing to do for your product. Each extra options massively increases the number of ways in which the code can interact and the number of tests which have to be carried out so there is a significant cost attached. In the enterprise space you will have to accept that clients will make demands in this area but you need to accurately assess the consequences and costs (one off during development and on-going for support) and make sales and management aware of them.
But essentially they all come down to the same thing - product software, even on the enterprise level, is far far cheaper than having an in-house team (or consultancy) build something bespoke. That price advantage comes with a downside - it's that you don't get exactly what you want and that the business needs to flex to the software sometimes.
It's not usually a popular message with clients or with sales but you need to work out which market you're in (product or bespoke) and remember that when making decisions.
In terms of the other two bits of the question - I don't believe the context created it at all. The root of it is that organisations are different. Unless you have all your clients the same, it was always going to be a problem at some point. Maybe it's a bit worse than it might have been but probably less than you think.
My experience in this area: I've been on both sides of the fence. I've been a development and / or project manager commissioning enterprise (and non-enterprise) third party software products (portals, finance systems and travel booking systems) and I've worked for two software houses developing them as a development manager (which is currently what I do).