At the very least, it will drive a wedge in your trust with him.

He will need to prove himself to you moving forward that he can be 100% honest with you.

And you may always have in the back of your mind, is he being honest and will he be faithful?

Not coming out with the whole truth does erode at trust. There's no way around it.

So if you decide to move forward with him, know this.

It may take time for you to fully trust him again, and that will take him always being upfront with you every single time about everything. You may still not fully trust him though.

And I agree that you don't have to accept it or him just because he accepts YOU.