I have learned that it matters more what they do rather than what they say. Words can be improvised or rehearsed, genuine or fake, direct or indirect. Pretty wishy-washy in terms of what we mean/could mean/might mean/do or didn't mean. However, our actions say a lot more.
Think about it. We can have an excuse for just about every behavior. But at the end of the day, we still engage in said behavior. For example: if you're on a diet and you just pigged out you might say " Well, I've been good so far on my diet. This won't hurt" or "I'll run an extra mile" or "I deserved this today." BUT, after all is said and done, you still cheated on your diet. You still didn't follow the rules. You still did what you weren't supposed to, even if you can come up for reasons why did it.
Same can be said about your boyfriend. He can tell you he was bored, that he would NEVER cheat on you, that he doesn't find yoooou boring etc. but at the end of the day, he still took every second of his time to register to a hook up site. Out actions are sometimes something we CAN'T cover up with double speak and excuses. They are blatant.
The truth is, he didn't expect you to find out. If he did, he would have said to you first "I was bored. Look what I registered for." But he didn't and I assure you that you'd be none the wiser had you not find out for yourself. You put him on the spot and he gave you a generic excuse that frees him from accountability. "I didn't do it, my BORED self did it. Shame on him. Non-bored self would NEVER do such a thing." And you buy it.
Love is a complicated thing no doubt, and even when we are faced with what seems like the obvious decision (dump him, deserve better, etc) we doubt ourselves still. You might still feel love for him but that doesn't mean something like this isn't a red flag and because of this "love", you are willing to overlook it and underplay what is a blatant red flag of what is to come. Hey, I get it. It's not always black and white, but sometimes our instinct think more clearly than our love-goggle-wearing heart. Surely he does love you. But did he respect you and the relationship? No. And isn't respect synonymous with love? You can't say "I love you, but let me get on this hookup site real quick."
It isn't so much just THIS act of a tinder account that you have to get over. You'd be mistaken if you think so. Because more likely than not, something similar to this will find its way to peeks its head out of the water one way or another, in a different shape, size, and form.
Try to work it out or not. "Trying" to sustain this sinking ship is all you will be doing from now on. Damage is done and its only a matter of time. His fault 100%. Hope you get the strength to make the right decision.