This is absolutely correct. That is what "Recusal" is all about. If you feel you cannot engage fairly in the political process, then you are obligated to recuse yourself.
But then surly you believe the vast majority of republicans voting is paramount to a form of abuse? Are you against people exercising their right to vote?
Not everyone has the right to vote on everything already, obviously. Not every vote is carried out to execution, for similar reasons. And votes that are executed are occasionally rescinded because democracy is a tool, not a goal, and when those who participate in it do so with intent to undermine it, those attempts must be opposed.
Congress-members have a right to vote on legislation, but yes - I'm opposed to them exercising that right on legislation in which they are personally involved, especially if they know they are incapable of participating fairly in the legislative process because of some sort of conflict of interest or simply because they know the topic makes them to emotional to make wise decisions in regards to it's legislation.
Recusal is simply what a responsible and reasonable person does, when an important decision is happening and they know that their participation is likely to make things work - they recuse themselves, and leave others who are more capable of sanely moving the topic forward to carry the day (assuming such a fallback system is in place, of course - if there's no better alternative, recusal may be a mistake).
There are different standards at different levels of the process though. Voting in, say, a congressional or parliamentary election, generally has little in the way of obligations. It is intended to be an expression of the people's preference in representatives, and thus it would be quite hard to "abuse" such a vote. And to the extent it might be (voting for family members and friends, simply because they are family members and friends instead of because you think they would represent you well) the effect is minimal, so as a general policy there's not much point. If you were intending to vote for someone simply because you think they would do a bad job in that position but it would give you some personal benefit - yes, I think it would be wrong to cast that vote. There's no realistic way to enforce this sort of thing though, and little benefit in trying at this level.
But once you have been elected, you are elected with the expectation of fulfilling certain duties, and if you cannot act in such a way so as to properly fulfill those duties, you should not exercise your right to vote on the results.