Yes, the GOP will have some sort of future, though they will need to adapt their platform to the changing times. All countries, even places with only two major parties, always have a party that is more conservative and right-wing. But it is possible that GOP power will continue to wane somewhat if they do not make changes, especially as old people die off.
America fully supports conflicting ideas and will always have them. Living on the northern end of the East Coast, Democrats outweigh Republicans considerably, but elsewhere in the country is a different story. There will always be staunch Republicans looking to maintain what they consider American traditions, but if they have a real future is a different story.
The GOP has become ridiculous and a parody of a real conservative body. It has allowed extremist and patently ignorant forces to high jack policy direction and had become a nasty, vindictive party that does not work in the best interests of the American people. In fact, the extremist rhetoric, filled with outright lies actively harms Americans.
During the last election, the GOP revealed how racist they are as they chose a white VP candidate even though they knew that picking someone from a minority group would have given them an edge.
Now with all these massacres going on in public places and schools, they are reluctant to detach themselves from the NRA. Defending the interests of the gun industry takes precedence over schools' safety for the republican leaders.
The GOP as it exists right now has no future. There is far to much fighting among the party that draws away from the large issues the party faces. If the GOP continues to fight each other and cannot unify around a set of causes then there is simply no hope for them. It has said that a house divided against itself cannot stand and the same holds true for a political party.