is it wrong to assume that a 100% degree of belief implies that no amount of evidence can change your mind?
You can think of this as a definition rather than an assumption. Within the Bayesian calculus, degrees of belief are handled like this. It is fair enough that you personally would like to handle it differently, however then Bayesian calculus doesn't fit as a model for your thinking.
Accepting it, you may wonder whether you should always avoid assigning 100% probability to anything that is not logically impossible (a Bayesian may say so), but see below.
A zero prior is not recommended even for theories that have had no evidence so far.
In fact, in applied statistics, prior probabilities of one are routinely assigned to nontrivial (and for sure not certain) events such as data being exchangeable, or following certain specific parametric models. In such situations still every isolated observable event can have a probability that is neither zero or one (for example in an exchangeable model with normal distributions), however implicitly assumptions are being made about the underlying process that may not be appropriate.
For example, if you observe binary events, exchangeability implies that if you observe 100 times 1, then 100 times 0, then 5 times 1 in a row, the probability for the next observation to be 1 is the same as had you observed 105 times 1 and 100 times 0 in seemingly random order. This doesn't seem rational, but if in fact you started from a prior assuming exchangeability, whatever sequence of outcomes you then observe, according Bayes' Theorem nothing can switch your beliefs away from exchangeability (in line with what you observed in your posting).
In fact this is a very valid criticism of applied Bayesian statistics (that can be found in some literature). One could respond that indeed "you should not assign probabilities of zero or one to anything conceivable", however in practice this may enforce prior assignments to be so complex that they are ultimately impossible to handle (there are manageable alternatives to exchangeability and even parametric modelling, but they will still exclude with probability 1 certain things that are by no means impossible).
A more practical response is, in my view, to admit that formal probability models are devices for learning rather than meant to be "true" in reality. This includes probability models for (subjective) uncertainty/belief. Such models will always simplify and never match perfectly what they are supposed to model. We may therefore tentatively use a model that assigns probability 0 or 1 to something potentially possible but not certain, as long as it helps us, but keeping in mind that it has the limitation to "forbid" certain things that could in fact happen; and if required, we may drop or update it.
Note that this will violate the Bayesian requirement of coherence, but it is often better to violate a certain "dogma" rather than sticking to it if it becomes apparent that it misleads us. (Some Bayesians would say that the original model, enforcing exchangeability, say, wasn't our "true" model in the first place, but just a convenient approximation of it, and may then claim that dropping it when encountering evidence against it still follows Bayesian logic with respect to some "true model" postulated to exist but not in advance properly formulated by us. This, however, is speculation, and can obviously not be checked because it's post hoc.)
If you have some time in your hand, you may enjoy this (which despite the title also has something about Bayesian/epistemic probability):
C. Hennig: Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-As-Model