If you're applying for a position of remote developer that has nothing to do with customer care (over the phone) what so ever I don't see how having a speech problem might cause issues.
Most of the communication happens over emails or some sort of chat (from Irc to Slack and from Skype to Discord) and with the diversity of accents and personal backgrounds people are pretty used to a variety of situations.
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If you're applying for a position of remote developer that has nothing to do with customer care (over the phone) what so ever I don't see how having a speech problem might cause issues.
Most of the communication happens over emails or some sort of chat (from Irc to Slack and from Skype to Discord) and with the diversity of accents and personal backgrounds people are pretty used to a variety of situations.