Tell them how much it's annoying you.
It's a difficult balance for them to get right. The reality is that it's much easier and cheaper to raise money from existing donors or people who have shown some interest, than by trying to interest everyone. So in a way, they are using your contribution efficiently to raise as much as they can.
Existing donors are very valuable though, especially if they stay with the charity for a long time. In the first year much of your contribution can go on the set-up admin, membership pack and so on, so it's usually from year 2 that you are valuable. Therefore they should really want you to stay. Keeping existing members is much more efficient than recruiting new ones.
Reliable members are especially valuable for charities that rely heavily on raising funds from grants - always short-term and for a particular purpose - for which the 'unrestricted funds' from memberships give them freedom to pursue their core charitable objectives, as well as to use as the core funding to match a big grant against. Membership numbers are important to campaigning charities too.
So, it's in their interests to keep you and if they are behaving in a way that puts you off, it might help to tell them, or they'll never know and pull the balance back to something more acceptable.
Btw OP, I believe I remember you from your moving house thread and happen to know that, if you'd like to swap your penguin for an otter, there are some nice, very non-hassly people locally who could do that for you!