This is very contextual, and there is no one right answer.
Upfront it's important to recognize marketing and design have different and sometimes opposing roles. Designers attempt to make a coherent, fun game experience. Marketing attempt to make money off it. Both are crucial to the success of a game and the survival of the folk making it.
Before you fight with marketing folk, it helps to try understand them and try and speak their lingo. Giving clear, rational responses to their concerns and bringing up your concerns in their language can go a long way towards resolving conflicts.
Marketing is typically driven by the current market realities as determined by empirical data. The degree to which they look at new trends in the market may vary depending on who is doing the marketing, but typically marketing folk won't take well to unproved ideas or designs.
When drawing a line in the sand it may be helpful to consider a number of factors:
1] Can you compete in the market with your current design? If competitor X completely outclasses your game, a marketing driven design changes may actually be helpful!
2] At what stage are you in development? :
Early stage: design changes now can make your game more appropriate for your target demographic, make you better able to compete, but can also homogenize your design to such a degree that your game is not differentiated in the market place. The concept of differentiation is one that marketing folk understand so try to explain your ideas in terms of differentiation.
Mid->Late stage: design changes at this stage can yield wasted work (very quantifiable, just take axed features and multiply by number of devs it took and how much it cost the company for each dev). Moreover, design changes at this stage could push the schedule out, forcing you to miss important marketing dates.
3] Is the marketing requested change reasonable? Is it trivial or is it core to the whole game design thus far? If it's trivial, sometimes it's easier to bite the bullet. If you're dealing with unreasonable requests of a core nature, you're probably out of luck and no attempt to rationalize things is going to get you very far. In these cases, unless you're the boss it's probably best not to expend the effort fighting it - just try to protect yourself against future blame by making it clear this was not your design change.
Given these factors then, the question then becomes: how do I shield myself from the risk of design changes? Almost certainly it involves a whole bunch of cheap upfront work, normally called preproduction, during which a game is prototyped, and it's fun is proved, and market viability is tested before it is actually built.
Just to note that despite what I've said here, there are often strict communications channels in game organizations. Designers typically communicate through their leads, as do coders and artists. Also design changes driven by marketing or by design, should strictly go through coder leads, art leads and marketing before they're set in stone. this is important so that all the major stakeholders can review the viability of the design and how it impacts their schedule.