Getting back to the issue (thank you, Sharper):
We have three possible sentences here:
a) Since they have been joining the drama club they have discovered their love of acting.
b) Since they have joined the drama club they have discovered their love of acting.
c) Since they joined the drama club they have discovered their love of acting.
xxbubbliexx only mentioned the first two, and the second part of the sentence is apparently not part of the controversy between xxbxx and her/his teacher (and that it should be in present perfect is perfectly clear).
(@mary nz/a, #26: I read Es geht mir in diesem Fall nur darum, ob ich Progressive oder Simple gebrauchen muss as "do I need the progressive perfect tense in the first part of the sentence, or is a simple present perfect better?" But just in case xxbxx meant 'simple past', which does not appear in any of the examples, I've added the third variant above. I don't understand what you mean by saying the OP mistakenly used present perfect instead of present simple in his/her version.)
The construction is:
since [point in time] [Subject]+[Verb in perfect tense].
since I was born, since 1986, since I joined the club, etc.
The 'point in time' may also contain a verb (since I was twelve, since I joined the club), and this may lead to confusion.
"since is used with a point in time and means 'from that point to the time of speaking'. It is always used with a perfect tense." (Thomson/Martinet, A Practical English Grammar)
Therefore, JGMcI, your worries in #20 are unfounded (This breaks the rule I always recommend, namely that when a point in time is indicated, the simple past is used. However, I think we can make an exception to that rule because 'their love of acting 'continues.). No rule is broken. The verb (they have discovered...) does not refer to a point in time, but to a period from a point in time up to the time of speaking which is indicated by since. There is a difference between 'In 1984 I discovered...' and 'Since 1984 I have discovered...', and only the first example indicates a point in time. The second one indicates a period which began at a certain point in time.
Also, @Mary nz/a in #21: Ok, so you know the rule "present perfect tenses after since" - well learned, but that doesn't apply here, unfortunately. Of course it does. I was glad to see that you silently corrected your statement by 'adding' later that the first verb after 'since', in this case, is used to denote a past point in time while the present perfect verb is in the next part of the sentence, but it would have been much clearer (at least to a student of English who is in a discussion with her/his teacher) if you had explicitly revoked your first statement. I still have to come across a sentence in which this rule does not apply.
Now, all native speakers of English in this discussion (and, Mary, all experienced speakers of English who happened to learn German first) agree that variant a) is wrong, unidiomatic, not even colloquially acceptable, ungrammatical. Is this a possible unequivocal message to xxbumblebeexx or whatever this nick is ;-)? -- namely,
"Since they have been joining the drama club ..." is wrong.
Which leaves b) and c), "Since they joined...." and "Since they have joined..."
From the original query: Meine Lehrerin allerdings war der Meinung, dass to join in diesem Fall das Mitglied sein [Mitgliedsein] bezeichnet. This actually sounds like a defence of 'have joined' vs. 'joined', but doesn't justify the 'have been joining'. There is a notion that to join a club means you are a member, and while the act of joining is a past point in time (to become a member at a given date), the implication of this act of joining is a membership dating from this point in time. IMO, you wouldn't use 'I joined this club' on its own, i.e. without a time specification, but I see that 'I have joined this club' imparts a vivid sense of being a proud member, being an active member.
I agree with Mary nz/a, Gibson, and others that 'Since they joined the drama club' is correct. But I can see the idea behind 'since I have joined', and apparently many speakers of English use it that way because the particular verb 'join' has implications (to be henceforth) which most other verbs don't have. (This applies to some of the internet examples dude provided in #25.) When a manager of a football club says 'Greatest win since I've been here', that's OK, but it is informal or colloquial language. Some Goo-research has more or less convinced me that present perfect as the description of the point of time which 'since' demands is rare and usually appears in personal statements such as blogs or letters to the editor, and it is also pretty much limited to verbs such as 'join' and 'be'. Present perfect as a tense following a since+point in time-statement is undisputed.