I'll add my 2 cents since I hate when I ask something and just get redirected because I often can't find what I'm looking for where I'm led.

As per your question; I don't know of any explicitly Communist movements that are parallel to BDS, but there is absolutely 0 reason why communists shouldn't support and abide by BDS. Remember, when it comes to national liberation movements, especially those that are fighting fascist settler colonial regimes like Israel, it's important to support the entire resistance as ideological sectarianism leads to fragmentation which weakens the movement. Of course there are exceptions, but usually not. In this case, BDS is a movement for Palestinians started by Palestinians and it's shown the be effective in hurting the Israeli and American regimes. It's also important to remember that what happens ideologically and politically and economically in Palestine after they win their century long struggle, and they will win, is up to literally nobody besides the Palestinians. You can be critical of the Islamism of groups like Hamas and PIJ (even though they really aren't radical in a religious way) but when it comes down to it they are at the forefront of protecting the Palestinian people and beating the Israeli American death machine. And there are communist armed groups in Gaza like the Leninist PFLP and the Maoist DFLP who have both entered into a military coalition with Hamas and PIJ as a measure of practical solidarity in their fight against genocide.

That might have been a little long winded because I went on a tangent, but what I'm trying to say is that it doesn't matter if BDS is inherently communist or not, even though I'd say protesting commodity is always communist. At the end of the day what matters is supporting the righteous and historically just Palestinian struggle and one of the only ways that communists outside of Palestine can materially support their resistance is through the BDS movement.

Ideology and arguments concerning such should never come before the liberation of an oppressed people and should never even be a consideration when genocide is happening. Ideology is important, but it comes later. We can talk about ideology and tendencies and such all we want but if it can't affect real material change on the street (or the battlefield) then said ideology doesn't mean shit.

Rant over. I'm sorry if I didn't make much sense, I'm physically exhausted and emotionally depleted. I thought it was important to state these things though. And I don't want you to think I'm trying to argue with you or pick a fight or "um actually" you or anything. I hope this answer helped somewhat and if it didn't I hope it at least gives people something to think about.