clusters in example input are 12 (0 and 11 - 10 repeated) and expected output has only two clusters and organisms in input are 2 and in expected output are 4. Can you post matching input and output?

This can be done outside R. I replaced | with tabs using sed, renumbered rows as there were duplicates and added few more clusters to example OP data (given below).

in R: output with modified OP data:

> xtabs(~V1+V2, test)
    V2
V1   org1 org2 org3 org4
  0     0    0    0    1
  1     0    1    0    0
  2     1    0    0    0
  3     0    0    0    1
  4     0    0    1    0
  5     1    0    0    0
  6     1    0    0    0
  7     0    0    1    0
  9     1    0    0    0
  10    0    0    0    1
  11    0    1    0    0

outside R (with datamash and miller), output with modified OP data:

$ datamash -s crosstab 1,2 --filler 0 < test2.txt  |sed '1 s/^/Cluster No\./g' | mlr --itsv --otsv sort -n "Cluster No."

Cluster No. org1    org2    org3    org4
0   0   0   0   1
1   0   1   0   0
2   1   0   0   0
3   0   0   0   1
4   0   0   1   0
5   1   0   0   0
6   1   0   0   0
7   0   0   1   0
9   1   0   0   0
10  0   0   0   1
11  0   1   0   0

modified data:

$ cat test2.txt 
0   org4    gene759
1   org2    gene992
2   org1    gene1101
3   org4    gene757
4   org3    gene1702
5   org1    gene989
6   org1    gene990
7   org3    gene1699
9   org1    gene1102
10  org4    gene2439
11  org2    gene1374