Programming :: Script To Delete Aligned Single-character Columns With No Field Separator?

The lines beginning with greater-than symbols are the sequence descriptors and the lines immediately after each descriptor with A-Z characters, dashes, and question marks are the aligned DNA sequences. The sequences are always the same length within a file and never span/wrap across more than one line.I am trying to write a script to remove positions in the sequences that are only represented by a -, X, ?, or N (these represent gaps or missing data). Also, if there is exactly one non-gap/missing character in a position it is also useless (there is nothing to compare it to) so I would like to remove those positions as well.

Position 5 (from the left) was removed because it was all gap/missing characters. Position 9 was removed because only one character was a non-gap/missing character. Position 10 was retained because there were 2 non-gap/missing characters.I'm really not sure where to start here. My first concern is I can't figure out how to tell awk to treat each character in lines not containing a greater-than symbol as a separate field. After that, I'm thinking I should use set up a counter to count the number of lines with gap/missing characters comparing that to the total number of lines not containing greater-than signs?