Will the research activity during my Master's program seriously impact my PhD or career path?
The further you are in your studies, the more your track record will dictate where you go. But I think that you are not at a point that experience in a related field is going to harm you. And, if you do things cleverly, you can gain very relevant experience.

For instance, you can gain experience in a relevant programming language doing bioinformatics (which is basically open to any programming language), and this technical experience will be relevant to any computational work you do. This seems like a great opportunity to gain that experience while improving your academic track record. I believe that in both these fields a PI will be most interested in someone with technical knowledge (given that a PhD in applied CS is not a course in CS), and luckily for you, this knowledge is independent of whether you are studying genes or phonemes (sorry for that terrible pun).

It's really rare in academia to be able to do exactly what you want. You'll always be carrying out research under someone else's vision, and rather than trying to find the perfect position or such, you just need to find a way to shine in that project/position/etc. As I said above, I believe that the credit and technical experience you will gain in this current position will be relevant for computational linguistics also, especially given the stage you are at. If there is a time to diversify your abilities, earlier is better. At a later stage this will have different consequences.

So I think you should take the bull by the horns and learn as much as you can. I can't imagine someone turning you down from a PhD because of being involved in a computational project simply because it doesn't perfectly overlap their field. All these computational-related fields have a huge overlap nowadays, and computational linguistics is in itself an interdisciplinary field.