Hmm, tricky one, is it just the job title that's different or is the new job structurally/hierarchically lower down than the old one, i.e. were you previously 'head of marketing' and the most senior marketing person in the organisation, and now you are 'deputy head of marketing' but there's also a 'head of marketing', an 'assistant director of marketing' and a 'director of marketing' as well? I can def see the latter would take some getting used to if you were used to having full accountability and autonomy to do whatever you thought best in your area of expertise and now you are swathed in layers of governance and hierarchy and different people having to be consulted and got on side before you can do anything? Not that one or the other is the 'right' way to do things, obviously in big organisations and with large budgets there will be more bureaucracy and 'layers' than smaller ones, some people do just prefer working in one way over the other, sometimes it's just an adjustment period, sometimes it may be that actually you need to move back towards the way you naturally prefer, take from this job what you can and look at when/how you make your next steps?
Either way though, people should not be being rude and putting down your suggestions. I work in what's usually thought of as quite an old fashioned and hierarchical type of organisation (public sector) and we would never ever 'put anyone in their place' for making suggestions, whether that person was the most junior admin person or the director. Obviously the helpfulness of the suggestions can vary (although frankly those from the admin people are usually a hell of a lot more useful than those from the director 
), but there's no excuse for incivility and making someone feel small. If that happens on a regular basis I would be either talking to the individuals concerned or my manager about it because it's not acceptable.
I do have to say though (as a veteran of hierarchical organisations, including ones that don't seem so on the outside) that people can be a bit funny and defensive about 'new people' and their 'suggestions'/ideas/advice, particularly if said new person is seen to be a bit 'above their station' for whatever reason, because they've got more/less experience/qualifications than others, or are younger/older than others or 'face doesn't fit' type situations. I'm not saying it's right or pleasant, at all, but what's behind it is usually more to do with the recipient than the suggestion, if you see what I mean. People are often a bit scared of change and/or fearful for their own jobs and reputation if the new person could be seen as a threat to them and it makes them go very defensive and odd. You can be a bit 'damned if you do damned if you don't' because if you don't mention anything about your past experience and qualifications it's 'who's she to tell us what to do' whereas if you start a meeting or conversation with a potted history of your CV, academic qualifications and job achievements you naturally seem boastful and weird because who does that .
To reassure you though, usually it goes away after a while if you gently persist and don't get discouraged. Once they get to know you and see that everything is still OK, the world hasn't fallen in etc and once you get to know the right way to work around particular individuals and how/when to present things to them, frankly play the game a bit, frustrating as that is, it goes away and ta-da, you are accepted - it's the next new person that then gets looked on with suspicion and in fact you may find you become flavour of the month in comparison which is a whole other weird thing to deal with!