According to the gutenberg handbook you can use the blocks.registerBlockType filter which allows you to play around with the block settings.
For most of the wp core blocks modifying the supports.align property works pretty well:
wp.hooks.addFilter(
'blocks.registerBlockType',
'my-theme/namespace',
function( settings, name ) {
if ( name === 'core/pullquote' ) {
return lodash.assign( {}, settings, {
supports: lodash.assign( {}, settings.supports, {
// disable the align-UI completely ...
align: false,
// ... or only allow specific alignments
// align: ['center,'full'],
} ),
} );
}
return settings;
}
);
In my tests this worked for most of wp core blocks, except for core/image, core/paragraph, core/heading and core/quote.
Troublesome Image Block
As for WP 5.0.3 (and at least up to 5.3) these blocks will receive an additional alignment control like this:
with code:
...
{
align: ['left','full'],
}
...
To control the available alignments for the core/image block, you would have to modify the edit method of a block using the editor.BlockEdit filter.
Nasty Headings, Paragraphs & Quotes
The problem with core/paragraph, core/heading and core/quote is, that block-align (defined by classenames alignleft, alignwide, … in the frontend and the data-align attribute in the editor) is not clearly separated from the text-align (defined in the style attribute), which leads to odd results like this:
[UPDATE 2019-11-13]: As of WP 5.3 this works pretty well with core/cover now.