The isMobile function doesn't need to be a function with a nested IIFE and a closure. Just run it:

  isMobile = do ->
    userAgent = navigator.userAgent or navigator.vendor or window.opera or ""
    /.../.test(userAgent) or /.../.test(userAgent.substr(0,4))

Now, isMobile is just a boolean value. The do keyword means it's evaluated immediately. Note I've also added a "" fallback for userAgent just in case. Since you might call substr on userAgent, it must be a string, or the script will just fail.

You changeTextInputToDate doesn't actually change the inputs, really. It replaces them. But changing them seems much easier:

  changeTextInputToDate = (inputs) ->
    inputs.each -> $(this).attr type: 'date'

(I'm using this instead of @ just because I always think @ looks weird by itself. I like using it as a prefix for things, but if I'm referring to the this object itself, I prefer to use this. Just personal preference.)

In dataTableFooterCallback it'd be nicer to fetch the column once, since that's what you need for the expressions. I'd also make the footer callback a nested function in initializeDataTable, too. Especially as that function references @api, which doesn't make sense except in the context of a data table callback. So there's no reason for the function to float around in a wider scope:

  initializeDateTable = (element) ->
    footerCallback = ->
      column = @api().column(1)
      total = column.data().map(parseCurrency).reduce (sum, value) -> sum + value
      $(column.footer()).html "#{total.toFixed(2)} лв"

    element.DataTable
      columns: [
        { type: 'date', searchable: false }
        { type: 'currency-bg', searchable: false }
        { type: 'string' }
        { type: null, orderable: false, searchable: false }
      ]
      footerCallback: footerCallback
      order: [[0, 'desc']]
      paging: false
      dom: 't'

You'll note a few more changes:

• I'm using explicit { and } around objects in the columns array, rather than relying solely on whitespace - makes it easier to read, I think.
• I'm using map + reduce, rather than doing all the work in the reduce callback. This makes for a simpler expression, and eliminates sumCurrency completely.

parseCurrency I'd write as

parseCurrency = (value) ->
  switch typeof value
    when 'number' then value
    when 'string' then (value.match(/\d+(\.\d+)?/)?[0] or 0) * 1
    else 0

The ?[0] or 0 guards against match returning null. Without the null-coalescing ? your script just fails as null[0] doesn't work.

The isMobile function doesn't need to be a function with a nested IIFE and a closure. Just run it:

  isMobile = do ->
    userAgent = navigator.userAgent or navigator.vendor or window.opera or ""
    /.../.test(userAgent) or /.../.test(userAgent.substr(0,4))

Now, isMobile is just a boolean value. The do keyword means it's evaluated immediately. Note I've also added a "" fallback for userAgent just in case. Since you might call substr on userAgent, it must be a string, or the script will just fail.

You changeTextInputToDate doesn't actually change the inputs, really. It replaces them. But changing them seems much easier:

  changeTextInputToDate = (inputs) ->
    inputs.each -> $(this).attr type: 'date'

(I'm using this instead of @ just because I always think @ looks weird by itself. I like using it as a prefix for things, but if I'm referring to the this object itself, I prefer to use this. Just personal preference.)

In dataTableFooterCallback it'd be nicer to fetch the column once, since that's what you need for the expressions. I'd also make the footer callback a nested function in initializeDataTable, too. Especially as that function references @api, which doesn't make sense except in the context of a data table callback. So there's no reason for the function to float around in a wider scope:

  initializeDateTable = (element) ->
    footerCallback = ->
      column = @api().column(1)
      total = column.data().map(parseCurrency).reduce (sum, value) -> sum + value
      $(column.footer()).html "#{total.toFixed(2)} лв"

    element.DataTable
      columns: [
        { type: 'date', searchable: false }
        { type: 'currency-bg', searchable: false }
        { type: 'string' }
        { type: null, orderable: false, searchable: false }
      ]
      footerCallback: footerCallback
      order: [[0, 'desc']]
      paging: false
      dom: 't'

You'll note a few more changes:

• I'm using explicit { and } around objects in the columns array, rather than relying solely on whitespace - makes it easier to read, I think.
• I'm using map + reduce, rather than doing all the work in the reduce callback. This makes for a simpler expression, and eliminates sumCurrency completely.

parseCurrency I'd write as

  parseCurrency = (value) ->
    switch typeof value
      when 'number' then value
      when 'string' then (value.match(/\d+(\.\d+)?/)?[0] or 0) * 1
      else 0

The ?[0] or 0 guards against match returning null. Without the null-coalescing ? your script just fails as null[0] doesn't work.